We provide surface areas and volumes practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on surface areas and volumes skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of surface areas and volumes Questions

Question No | Questions | Class |
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1 | If the volume of a cube is ( 3 sqrt{3} a^{3} ) then total surface area of the cube is A ( cdot 6 a^{2} ) B . ( sqrt{3} a^{2} ) ( c cdot 18 a^{2} ) D. ( 6 sqrt{3} a^{2} ) | 9 |

2 | Find the total surface area of a cuboid whose length, breadth and height are 20 ( mathrm{cm}, 12 mathrm{cm} ) and ( 9 mathrm{cm} ) respectively | 9 |

3 | A sphere of radius ( 3 mathrm{cms} ) is dropped into a cylindrical vessel of radius ( 4 mathrm{cms} ). If the sphere is submerged completely, then the height (in ( mathrm{cm} ) ) to which the water rises, is A . 2.35 B. 2.30 c. 2.25 D. 2.15 | 10 |

4 | Find the depth of a cylindrical tank of radius ( 28 m, ) if its capacity is equal to that of a rectangular tank of size ( 28 m times 16 m times 11 m ) | 9 |

5 | Write the number of surfaces of a right circular cylinder. | 9 |

6 | A water tank of capacity ( 3000 L ) is filled with ( 1216 L 50 m L ). Find the volume of water which is required to fill the tank. | 9 |

7 | Find the volume of the sphere whose surface area is ( 9856 mathrm{cm}^{2} ) | 9 |

8 | A hemispherical bowl has a radius 3.5 cm. Its volume ( mathrm{cm}^{3} ) | 9 |

9 | How many cubes each of surface area ( 24 c m^{2} ) can be made out of a cube of edge measure ( 1 mathrm{m} ? ) A . 165000 B. 125000 c. 180000 D. 155000 | 9 |

10 | Find the total surface area of the cuboid with ( l=4 m, b=3 m ) and ( h=1.5 m ) | 9 |

11 | A solid sphere and a solid hemisphere have the same total surface area. Find the ratio of their volumes. | 9 |

12 | A unit cube is cut into two equal halves by a plane section parallel to one of its faces. The total surface area of both the halves is A. 6 sq, units B. 7 sq, units c. 8 sq, units D. 9 sq, units | 9 |

13 | A road roller is cylindrical in shape . Its circular end has a diameter ( 200 mathrm{cm} ) and its width it ( 1.4 mathrm{m} ). Find the least number of revolutions that the roller must make in order to level a playground of dimensions ( 125 m times 20 m ) | 9 |

14 | If the circumference of the inner edge of a hemispherical bowl is ( frac{132}{7} c m, ) then what is its capacity? ( mathbf{A} cdot 12 pi c m^{3} ) В. ( 18 pi c m^{3} ) ( mathbf{c} cdot 24 pi c m^{3} ) ( mathrm{D} cdot 36 pi c m^{3} ) | 9 |

15 | A close cylindrical tank of diameter ( 14 m ) and height ( 5 m ) is made from a sheet of metal. How much sheet of metal will be required. | 9 |

16 | Find the surface area of a sphere of radius: ( mathbf{1 4} c boldsymbol{m} ) | 9 |

17 | State true or false: The number of persons that can be accommodated in a big hall of dimensions ( 40 m, 25 m, 15 m, ) assuming that each person requires ( 5 m^{3} ) of air are 3000 A. True B. False | 10 |

18 | A solid in hemisphere at the bottom and conical above. If the surface are of the part our equal, find the ratio of radius and height of conical part. | 9 |

19 | Find the total surface area of cubes having the following sides. ( mathbf{5} c boldsymbol{m} ) | 9 |

20 | The diameter of a solid hemisphere is ( 42 mathrm{cm} . ) Find its volume, curved surface area and total surface area. | 9 |

21 | The surface area of three conterminous faces of a furniture is ( 5,10,20 mathrm{q} . mathrm{cm} ) respectively. Find the volume of the cuboid. A ( cdot 2 sqrt{10} mathrm{cm}^{3} ) B . ( 20 sqrt{10} mathrm{cm}^{3} ) c. ( 40 sqrt{10} mathrm{cm}^{3} ) D. ( 10 sqrt{10} mathrm{cm}^{3} ) | 9 |

22 | A solid iron pole consists of a cylinder of height ( 220 mathrm{cm} ) and base diameter 24 ( mathrm{cm}, ) which is surmounted by another cylinder of height ( 60 mathrm{cm} ) and radius 8 cm. Find the mass of the pole, given that ( 1 mathrm{cm}^{3} ) of iron has approximately ( 8 mathrm{g} ) mass. (Use ( pi=3.14) ) | 10 |

23 | Assume ( pi=frac{22}{7}, ) unless stated otherwise. Find the volume of a sphere whose radius is (i) ( 7 mathrm{cm} ) (ii) ( 0.63 mathrm{m} ) | 9 |

24 | The given figure shows a solid formed of a solid cube of side ( 40 mathrm{cm} ) and a solid cylinder of radius ( 20 mathrm{cm} ) and height 50 ( mathrm{cm} ) attached to the cubes as shown. Find the volume and the total surface area of the whole solid [Take ( boldsymbol{pi}=mathbf{3 . 1 4}] ) A ( cdot 122700 mathrm{cm}^{3} ) and ( 15880 mathrm{cm}^{2} ) B. ( 126800 mathrm{cm}^{3} ) and ( 15880 mathrm{cm}^{2} ) c. ( 148900 mathrm{cm}^{3} ) and ( 15880 mathrm{cm}^{2} ) D. ( 148800 mathrm{cm}^{3} ) and ( 15880 mathrm{cm}^{2} ) | 10 |

25 | If the lateral surface area of a cube is ( 1600 mathrm{cm}^{2} ) then its edge is ( mathbf{A} cdot 15 mathrm{cm} ) B. ( 18 mathrm{cm} ) ( c .20 mathrm{cm} ) D. ( 24 mathrm{cm} ) | 9 |

26 | The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross- section. If the length of the wire is ( 36 mathrm{m} ) find the radius of its cross-section. A ( .0 .8 mathrm{cm} ) B. ( 0.5 mathrm{cm} ) ( c .0 .3 mathrm{cm} ) D. ( 0.1 mathrm{cm} ) | 10 |

27 | A sphere of radius 3 ems is dropped into a cylindrical vessel of radius ( 4 mathrm{cms} ). If the sphere is submerged completely, then the height (in ( mathrm{cm} ) ) to which the water rises, is A . 2.35 B. 2.30 c. 2.25 D. 2.15 | 9 |

28 | The radius of Jupiter is ( 7.1 times 10^{3} m ) and that of the Earth is ( 6.3 times 10^{6} m ) Compare the volume of the two. | 9 |

29 | A solid hemisphere is mounted on a solid cylinder, both having equal radii. If the whole solid is to have a fixed surface area and the maximum possible volume, then the ratio of the height of the cylinder to the common radius is A . 1: 1 B. 1: 2 c. 2: 1 D. ( sqrt{2}: 1 ) | 9 |

30 | Three solid spheres of copper, whose radii are ( 3 mathrm{cm}, 4 mathrm{cm} ) and ( 5 mathrm{cm} ) respestively are melted into a single solid sphere of radius R. The value of R is A . ( 12 mathrm{cm} ) B. ( 8 mathrm{cm} ) ( c .4 mathrm{cm} ) D. ( 6 mathrm{cm} ) | 9 |

31 | 51. A parallelopiped whose sides are in ratio 2 : 4:8 have the same volume as a cube. The ratio of their surface area is : (1) 7:5 (2) 4:3 (3) 8:5 (4) 7:6 | 9 |

32 | 58. A prism has as the base a right- angled triangle whose sides adjacent to the right angles are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 gm/cubic cm. The weight of the prism is (1) 6.4 kg (2) 7.2 kg (3) 3.4 kg (4) 4.8 kg | 10 |

33 | Find the height of a cylinder that has a diameter of 10 feet and a surface area of ( 220 f t^{2} . ) Round your answer to the nearest whole number. (use ( pi=22 / 7 ) ). ( mathbf{A} cdot 0.1 mathrm{ft} ) в. 3 ft ( c cdot 2 f t ) D. ( 1 mathrm{ft} ) | 9 |

34 | The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas. | 9 |

35 | A road roller of length ( 3 l ) metres and radius ( frac{l}{3} ) metres can cover a field in 100 revolutions, moving once over. The area of the field in terms of I is ( (pi) l^{2} m^{3} ) | 9 |

36 | If the volume of a sphere is numerically equal to the surface area of the sphere, then find its radius. | 9 |

37 | Find the difference between total surface area ( & ) curved surface area of a hemisphere of radius ( 21 mathrm{cm} ) ( mathbf{A} cdot 1376 mathrm{cm}^{2} ) B . ( 1386 mathrm{cm}^{2} ) ( mathbf{c} cdot 1396 mathrm{cm}^{2} ) D. ( 1404 mathrm{cm}^{2} ) | 9 |

38 | A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is ( 8 c m ) and the total height of the cup is ( 11.5 mathrm{cm} ). Find the total surface area of the cup. (Take ( left.pi=frac{22}{7}right) ) | 10 |

39 | Assertion No. of spherical balls that can be made out of a solid cube of lead whose edge is ( 44 mathrm{cm}, ) each ball being ( 4 mathrm{cm} ). in diameter, is 2541 Reason Number of balls = (Volume of one ball)/(Volume of lead) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 10 |

40 | Two cubes have edge lengths in the ratio of 2: 3 respectively. The ratio of their surface areas is A ( cdot frac{4}{9} ) в. ( frac{8}{27} ) ( c cdot frac{2}{3} ) D. ( frac{sqrt{2}}{sqrt{3}} ) E ( cdot frac{sqrt{3}}{sqrt{2}} ) | 9 |

41 | The volume of cube is ( 36 mathrm{cm}^{3} . ) Its surface area is A ( cdot 6(36)^{frac{3}{2}} ) B. ( (36)^{frac{3}{2}} ) c. ( 6(36)^{frac{2}{5}} ) D. None | 9 |

42 | The surface area of a cuboid is ( 4150 mathrm{cm}^{2} . ) If its length and breadth are ( 35 mathrm{cm} ) and ( 25 mathrm{cm} ) respectively, find its height. | 9 |

43 | Find the area of the base of a box of height ( 4 mathrm{cm} ) and lateral surface area ( 120 mathrm{cm}^{2}, ) if its length is twice its breadth. | 9 |

44 | Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid is ( 648 mathrm{cm}^{2} ) find the length of edge of each cube. Also, find the ratio between the surface area of resulting cuboid and the surface area of a cube. A. ( 9 mathrm{cm} ) and 3: 1 B. 2 cm and 3: 1 c. ( 6 mathrm{cm} ) and 3: 1 D. ( 3 mathrm{cm} ) and 3: 1 | 9 |

45 | A swimming pool is ( 40 mathrm{m} ) long and ( 15 mathrm{m} ) wide. Its shallow and deep ends are 1.5 ( m ) and ( 3 m ) deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in litres required to fill the pool. A .42,33,000 litres B. 13,50,000 litres c. 22,17,000 litres D. 41,12,000 litres | 10 |

46 | If the total surface area of a solid hemisphere is ( 462 mathrm{cm}^{2} ), find its volume. Note: Take ( boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}} ) ( mathbf{A} cdot 716 ) B. 718.67 c. 720.87 D. 840 | 9 |

47 | Base surface area of a cylinder is 20 ( c m^{2} ) and its height is ( 10 mathrm{cm} . ) Find the volume of the cylinder. | 9 |

48 | A hollow hemispherical bowl of thickness ( 1 mathrm{cm} ) has an inner radius of 6 ( mathrm{cm} . ) Find the volume of metal required to make the bowl. | 9 |

49 | The, sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq. metres, its volume is : A ( .3180 m^{3} ) в. ( 4620 m^{3} ) ( c .5240 m^{3} ) D. None of these | 9 |

50 | A godown building is in the form as shown in figure. The vertical crosssection parallel to the width side of the building is a rectangle ( 7 m times 3 m ) mounted by a semi-circle of radius ( 3.5 m . ) The inner measurements of the cuboidal portion of the building are ( 10 m times 7 m times 3 m . ) Find the volume of the godown and the total interior surface area excluding the floor (Base) (Take ( boldsymbol{pi}=mathbf{2 2} / mathbf{7}) ) | 9 |

51 | Find the CSA and TSA of a solid hemisphere of radius ( 14 mathrm{cm} ) | 9 |

52 | A cylindrical tube of radius ( 12 mathrm{cm} ) contains water upto a depth of ( 20 mathrm{cm} . ) A spherical iron ball is dropped into the tube and thus the level of water is raised by ( 6.75 mathrm{cm} . ) The radius of the ball is A . ( 4.5 mathrm{cm} ) B. ( 6 mathrm{cm} ) ( c .7 .25 mathrm{cm} ) D. ( 9 mathrm{cm} ) | 9 |

53 | back. TUWW 4. The figure shows a cuboid with a volume of 180 cm3 by the -of 4cm 9 cm of (P + 3) cm in mo What is the value of p? baba | 10 |

54 | 57. There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of this pyramid is of length cm, then the volume of this pyramid is (1) 3a cm3 (2)3.acm3 cm (3) 3.3 (4) 6a cm | 10 |

55 | Find the radius of a sphere whose circumference and solid content have the same numerical value. | 9 |

56 | The volume of a sphere is ( 38808 mathrm{cm}^{3} ) Find its radius and surface area. | 9 |

57 | The height of cylinder is ( 4 mathrm{cm} ) The Radius of cylinder is ( 5 mathrm{cm} ) find its volume | 9 |

58 | A company packages its milk powder in cylindrical container whose base has a diameter of ( 14 mathrm{cm} ) and height ( 20 mathrm{cm} ) Company places a label around the surface of the container (as shown in the figure). If the label is placed ( 2 mathrm{cm} ) from top and bottom, what is the area of the label? | 9 |

59 | 66. The diameters of two ends of a bucket are 20 cm and 10 cm and its height is 24 cm. The volume (in cc) of the bucket is (1) 4000 (2) 4400 (3) 4040 (4) 1885 | 10 |

60 | If a sphere and a cube have the same surface area, then the ratio of the diameter of sphere to edge of the cube is A. ( sqrt{6}: sqrt{pi} ) (年) ( sqrt{pi} ). ( pi ) B. ( sqrt{pi}: sqrt{6} ) c. 2: 1 D. 1: 2 | 9 |

61 | 54. A toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and that of the cone is 3 cm and height of the cone is 4 cm. The total sur- face area of the toy (taking 1 = 22 7) is (1) 75.43 sq. cm. (2) 103.71 sq. cm. (3) 85.35 sq. cm. (4) 120.71 sq. cm. | 9 |

62 | A solid consisting of a right circular cone of height ( 120 mathrm{cm} ) and radius ( 60 mathrm{cm} ) standing on a hemisphere of radius ( 60 mathrm{cm} ) is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, (in ( left.m^{3}right) ) if the radius of the cylinder is ( 60 mathrm{cm} ) and its height is ( 180 mathrm{cm} ? ) | 10 |

63 | the radius of a solid hemisphere is ( 2 r ) Find its surface area. | 9 |

64 | Find the total surface area of cubes having the following sides. ( mathbf{5 . 5} boldsymbol{m} ) | 9 |

65 | The number of corners in a cylinder is ( A cdot 1 ) B. 2 ( c .3 ) D. None | 9 |

66 | Metal spheres, each of radius ( 2 mathrm{cm}, ) are packed into a rectangular box of internal dimensions ( 16 mathrm{cm} times 8 mathrm{cm} times 8 mathrm{cm} ) When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid (in ( c m^{3} ) ). Give your answer to the nearest integer. [Use ( boldsymbol{pi}= ) 3.14] | 9 |

67 | 71. Area of the floor of a cubical room is 48 sq.m. The length of the longest rod that can be kept in that room is (1) 9 metre (2) 12 metre (3) 18 metre (4) 6 metre | 9 |

68 | In a building there are 24 cylindrical pillars. The radius of each pillar is ( 28 mathrm{cm} ) and height is ( 4 mathrm{cm} . ) Find the total ( operatorname{cost} ) of painting the curved surface area of all pillars at the rate of ( R s .8 ) per ( m^{2} ) | 9 |

69 | If a largest sphere is inscribed in a cube of side ( 7 mathrm{cm} ) then find the volume of the sphere | 9 |

70 | Volume of a hollow sphere is ( frac{11352}{7} mathrm{cm}^{3} ) If the outer radius is ( 8 mathrm{cm} ), find the inner radius of the sphere. (Take ( pi=frac{22}{7} ) ) | 9 |

71 | In the rectangular solid in Figure 1 calculate the distance from vertex ( boldsymbol{A} ) to vertex ( boldsymbol{B} ) A ( cdot sqrt{65} ) B. ( 7 sqrt{2} ) ( c ) D. 1 | 10 |

72 | Find the total surface area of the following cylinders | 9 |

73 | A closed box made of steel of uniform thickness has length, breadth and height ( 12 mathrm{dm}, 10 mathrm{dm} ) and ( 8 mathrm{dm} ) respectively. If the thickness of the steel sheet is ( 1 mathrm{dm}, ) then the inner surface area is ( mathbf{A} cdot 456 mathrm{dm}^{2} ) B. ( 376 mathrm{dm}^{2} ) ( mathbf{c} cdot 264 mathrm{dm}^{2} ) D. ( 696 mathrm{dm}^{2} ) | 9 |

74 | Three solid spheres of diameter ( 2 c m, 12 c m ) and ( 16 c m ) are melted and made into a single sphere. Find the radius of the new sphere? | 9 |

75 | A solid metal cone with radius of base ( 12 mathrm{cm} ) and height ( 24 mathrm{cm}, ) is melted to form spherical solid balls of diameter 6 ( mathrm{cm} ) each. Find the number of balls thus formed. A . 30 B. 31 ( c cdot 32 ) D. 34 | 10 |

76 | What is the length of the sheet, 2 meter wide, required for making an open tank ( 15 mathrm{m} ) long, ( 10 mathrm{m} ) wide and ( 5 mathrm{m} ) deep? | 9 |

77 | An aquarium is in the form of a cuboid whose external measures are ( 80 mathrm{cm} times ) ( 30 c m times 40 c m . ) The base side faces and back face are to be covered with a coloured paper. Find the area of the paper needed? A. ( 3000 mathrm{cm}^{2} ) B . ( 5000 mathrm{cm}^{2} ) c. ( 8000 mathrm{cm}^{2} ) D. ( 7000 mathrm{cm}^{2} ) | 9 |

78 | Calculate the surface area of hemisphere having the radius of ( 1.4 mathrm{cm} ) A ( cdot 1.232 mathrm{cm}^{2} ) B . ( 12.32 mathrm{cm}^{2} ) ( mathbf{c} cdot 123.2 mathrm{cm}^{2} ) D. ( 1232 c m^{2} ) | 9 |

79 | Each face of a cube has perimeter equal to ( 32 mathrm{cm} ). Find its surface area | 9 |

80 | The outer diameter of a spherical shell is ( 10 mathrm{cm} ) and the inner diameter is 9 cm.Find the volume of the metal contained in the shell. Also find its outer surface area. | 9 |

81 | The internal and external diameter of a hollow hemi-spherical vessel is ( 24 mathrm{cm} ) and ( 25 c m ) respectively. The cost of paint one sq.cm of the surface is paise. Find the total cost to paint the vessel all over | 9 |

82 | Using clay, a student made a right circular cone of height ( 48 mathrm{cm} ) and base radius ( 12 mathrm{cm} . ) Another student reshapes it in the form of a sphere. Find the radius of the sphere | 9 |

83 | The radius of two cylinders are in the ratio 2: 3 and their heights are in the ratio ( 3: 5 . ) Find the ratio of their volumes. A ( cdot frac{2}{3} ) B. ( frac{3}{5} ) c. ( frac{4}{15} ) D. ( frac{3}{2} ) | 9 |

84 | Two spheres have their surface areas in the ratio 9: 16 Their volumes are in the ratio of A .64: 27 B . 27: 64 c. 16: 27 D. 11: 27 | 9 |

85 | The ratio of the volume and surface area of a sphere of unit radius: A .4: 3 B. 3: 4 c. 1: 3 D. 3: 1 | 9 |

86 | If a hemi-spherical dome has an inner diameter of ( 28 m, ) then its volume (in ( boldsymbol{m}^{3} ) ) is: A . 6186.60 в. 5749.33 c. 7099.33 D. 7459.33 | 9 |

87 | Find the volume of a hemisphere whose radius is ( left.7 mathrm{cm} . text { (use } pi=frac{22}{7}right) ) A ( cdot 112.66 mathrm{cm}^{3} ) в. ( 718.66 mathrm{cm}^{3} ) c. ( 12.66 mathrm{cm}^{3} ) D. ( 132.66 mathrm{cm}^{3} ) | 9 |

88 | Volume of a hemisphere is 19404 cubic ( mathrm{cm} . ) The total surface area is A. 2772 sq.cm B. 4158 sq.cm c. 5544 sq.cm D. 1386 sq.cm | 9 |

89 | Four cubic blocks with edge ( 4 mathrm{cm} ) were kept two on top of two and fused together into a block as shown. Find the total surface area of the block and the ( operatorname{cost} ) of painting it at ( R s .32 ) per ( c m^{2} ) begin{tabular}{|c|c|} hline 1 & 2 \ hline 3 & 4 \ hline end{tabular} A. ( R s .8992 ) B . ( R s .8092 ) c. ( R s .8192 ) D. ( R s .8190 ) | 10 |

90 | If the radius of a sphere is doubled, then its volume is increase by ( mathbf{A} cdot 100 % ) B. 200% ( c .700 % ) D. ( 800 % ) | 9 |

91 | A hemispherical tank is made up of an iron sheet of thickness ( 1 mathrm{cm} ). If the inner radius is ( 1 m, ) then find the volume of the iron used to make the tank. | 9 |

92 | Fill in the blanks: A point where three surface of a solid meet is called a | 9 |

93 | The total surface area of the cube is 216 sq. cm. The length of the longest pole that can be kept inside the cube is A ( .6 sqrt{3} ) B. 6 ( c cdot 8 ) D. ( 7 sqrt{3} ) | 9 |

94 | Find the lateral surface area and total surface area of the following right prisms. | 9 |

95 | If the total surface area of a solid hemisphere is ( 46 c m^{2}, ) find its volume | 10 |

96 | A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1: 2: 3 | 10 |

97 | Circumference of the edge of hemispherical bowl is ( 132 mathrm{cm} ). Find the capacity of the bowl | 9 |

98 | A soft drink can has a circular base with diameter ( 7 mathrm{cm} ) and height ( 12 mathrm{cm} . ) A powder tin has a square base with side ( 7 c m ) and height ( 12 c m . ) What is the difference in their capacities? A ( cdot 126 c m^{3} ) В. ( 132 c m^{3} ) ( mathrm{c} cdot 146 mathrm{cm}^{3} ) D. ( 150 mathrm{cm}^{3} ) | 9 |

99 | Small spherical balls, each of diameter ( mathbf{0 . 6} mathrm{cm}, ) are formed by melting a solid sphere of radius ( 3 mathrm{cm} ). Find the number of balls thus obtained. | 9 |

100 | An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is ( frac{1}{4} ) of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball. | 9 |

101 | Find the volume of a sphere of radius given below: ( mathbf{A} cdot 1,706.25 f t^{3} ) B. ( 1,766.15 f t^{3} ) ( c cdot 1,866.25 f t^{3} ) D. ( 1,766.25 mathrm{ft}^{3} ) | 9 |

102 | The radius of the cylinder whose lateral surface area is ( 704 mathrm{cm}^{2} ) and height ( 8 c m, ) is A. ( 6 mathrm{cm} ) в. 4 ст ( c .8 c m ) D. ( 14 mathrm{cm} ) | 9 |

103 | Three solid spheres of gold whose radii ( operatorname{are} 1 mathrm{cm}, 6 mathrm{cm} ) and ( 8 mathrm{cm}, ) respectively are melted into a single solid sphere. Find the radius of the sphere. | 9 |

104 | The radius of a sphere is ( 2.1 mathrm{cm} ). Find its surface area. | 9 |

105 | A sphere is melted and half of the molten liquid is used to form 11 identical cubes, whereas the remaining half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is ( A ) [ left(frac{4}{3}right)^{frac{1}{3}} ] в. [ left(frac{8}{3}right)^{frac{1}{3}} ] c. ( (3)^{frac{1}{5}} ) D. | 10 |

106 | Find the volume of a right circular cylinder if the radius of its base is ( 7 mathrm{cm} ) and height is ( 15 mathrm{cm} ) | 9 |

107 | The diameter of a sphere is decreased by ( 25 % ). By what percent its curved surface area decrease? | 9 |

108 | 66. The ratio of height and the di- ameter of a right circular cone is 3:2 and its volume is 1078 22 cc. then (taking * = ) its height is : (1) 7 cm (3) 21 cm (2) 14 cm (4) 28 cm | 9 |

109 | The internal and external diameters of a hollow hemispherical vessel are ( 24 mathrm{cm} ) and ( 25 c m, ) respectively. The cost to paint ( 1 mathrm{cm}^{2} ) surface is ( R s .0 .05 . ) Find the total cost to paint the vessel all over. (use ( left.pi=frac{22}{7}right) ) A . Rs.2100 B. ( R s .1867 ) c. ( R s .1245 ) D. None of the above | 9 |

110 | Sushant has a vessel, of the form of an inverted cone, open at the top, of height ( 11 c m ) and radius of top as ( 2.5 mathrm{cm} ) and is full of water. Metallic spherical balls each of diameter ( 0.5 mathrm{cm} ) are put in the vessel due to which ( left(frac{2}{5}right) ) th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant? | 10 |

111 | The total surface area of a solid cylinder is ( 462 mathrm{cm}^{2} ). Its curved surface area is one third of total surface area. Find the volume of the cylinder. A ( cdot 229 ~ c m^{3} ) В. ( 509 mathrm{cm}^{3} ) ( mathbf{c} cdot 439 mathrm{cm}^{3} ) D. ( 539 ~ c m^{3} ) | 9 |

112 | A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is ( 19 mathrm{cm} ) and the diameter of the cylinder is ( 7 mathrm{cm} ). Find the volume and total surface area of the solid. | 10 |

113 | Calculate the surface area(in ( c m^{2} ) ) of a solid cylinder with diameter ( 14 mathrm{cm} ) and Peight ( 10 mathrm{cm} .left(pi=frac{22}{7}right) ) | 9 |

114 | The total surface area of a cube is ( 486 mathrm{cm}^{2} . ) Calculate its edge | 9 |

115 | Find the volume of a sphere whose radius is ( 7 mathrm{cm} ) A. ( _{1437} frac{1}{3} c m^{3} ) в. ( _{1437} frac{1}{4} c m^{3} ) c. ( _{1437} frac{2}{3} c m^{3} ) D. ( _{1437} frac{1}{2} c m^{3} ) | 9 |

116 | A rectangular solid has a square base, with each side of the base measuring 4 meters. If the volume of the solid is 112 cubic meters, what is the surface area of the solid? A ( .144 mathrm{m}^{2} ) B . ( 250 m^{2} ) c. ( 172 m^{2} ) D . ( 228 mathrm{m}^{2} ) | 9 |

117 | The ( L=12 mathrm{cm}, b=10 mathrm{cm}, h=8 mathrm{cm} ) of a room. Find the total area of 4 walls. | 9 |

118 | A closed water tank has internal size of ( 10 m times 15 m times 20 m . ) It needs to be lined with waterproofing cement on all its internal side. At the rate of Rs. 250 per ( m^{2}, ) the total cost of lining will be Rs. A. 237,500 0 в. 325,000 c. 400,000 D. 475,000 | 9 |

119 | The side of a cube ( 4 mathrm{cm} ). Its area is A . 16 sq. ( mathrm{cm} ) B. 64 sq. cm c. 12 sq. ( mathrm{cm} ) D. None of these | 9 |

120 | The sum of the length, breadth and depth of a cuboid is ( 19 mathrm{cm} ) and the length of its diagonal is ( 11 mathrm{cm} ). Find the surface area of the cuboid. | 9 |

121 | A shotput is a metallic sphere of radius ( 4.9 mathrm{cm} . ) If the density of the metal is 7.8 g. per ( mathrm{cm}^{3} ), find the mass of the shotput. | 9 |

122 | Find a cylinder which would have the greatest volume for the given area ( S ) of its total surface. | 9 |

123 | The height of a room is ‘a’ and the areas of the two adjacent walls of a room are b’ and ‘c’. The area of the roof will be A ( cdot frac{b c}{a} ) B. ( b c ) c. ( frac{a c}{b^{2}} ) D. ( frac{b c}{a^{2} c} ) | 9 |

124 | If two cubes each of side ( 12 mathrm{cm} ) are joined end to end then the surface area of the resulting cuboid is A ( cdot 1728 mathrm{cm}^{2} ) B . ( 1440 mathrm{cm}^{2} ) c. ( 1445 mathrm{cm}^{2} ) D. ( 1450 mathrm{cm}^{2} ) | 9 |

125 | The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is ( 1056 mathrm{cm}^{2} ) and the volume of material in it is ( 1056 mathrm{cm}^{3} ). Find the sum of its internal and external radii. Given that the height of the cylinder is ( 21 mathrm{cm} ) | 9 |

126 | A 20 m deep well with diameter 7 m is dug up and the earth from digging is evenly spread out to form a platform 22 ( m times 14 m ) The height of the platform is ( mathbf{A} cdot 2.5 mathrm{m} ) B. ( 1.5 mathrm{m} ) c. ( 1 mathrm{m} ) D. 2 m | 9 |

127 | Three metallic solid cubes whose edges are ( 1 mathrm{m}, 2 mathrm{m}, ) and ( 3 mathrm{m} ) are melted and converted into a single cube. Find the edge of the cube so formed? A. ( 2.2 mathrm{m} ) B. 3.0 ( m ) ( c cdot 3.3 m ) D. 3.9 ( m ) | 10 |

128 | Find approximately the volume of the sphere of radius 1.001 | 9 |

129 | A right circular cylinder has Height as ( 30 c m ) and Radius as ( 35 c m ) find its ( boldsymbol{C S A} ) | 9 |

130 | The diameter of a solid metallic sphere is ( 16 mathrm{cm} . ) The sphere is melted and recast into 8 equal solid spherical balls. Determine the radius of the ball. | 10 |

131 | The dimensions of cuboid are in the ratio ( 3: 2: 1 . ) Its volume is ( 1296 m^{3} ) Find its height. ( mathbf{A} cdot 6 m ) B. ( 0.8 m ) ( c .6 mathrm{cm} ) D. None of these | 10 |

132 | A hemispherical bowl is made of steel, ( 0.25 mathrm{cm} ) thick. The inner radius of the bowl is ( 5 mathrm{cm} ). Find the outer curved surface area of the bowl | 9 |

133 | Find the total surface area of a solid hemisphere of radius ( 10 mathrm{cm} . ) [Use ( pi= ) 3.14] | 9 |

134 | If total surface area of a cube is ( 150 mathrm{cm}^{2}, ) find the edge. | 9 |

135 | Two cubes of edge ( 6 mathrm{cm} ) are joined to form a cuboid. Find the total surface area of the cuboid. | 9 |

136 | Assume that a drop of water is spherical and its diameter is one tenth of a cm. A conical glass has equal height to its diameter of rim. If 2048000 drops of water fill the glass completely then find the height of the glass | 10 |

137 | The figure shows the cross section of six identical spheres. The spheres, touching each other, are placed on a horizontal plane. The volume of each sphere is ( frac{32 pi}{3} c m^{3} . ) Calculate the length of ( boldsymbol{P Q}, ) in ( boldsymbol{c m} ) A . 18 B. 24 c. 36 D. 58 | 9 |

138 | The radius of the given figure below is 21 mi. Find its volume. (use ( pi=frac{22}{7} ) ). A ( .19,504 mathrm{mi}^{3} ) в. ( 19,404 mathrm{mi} ) C. ( 19,404 mathrm{mi}^{3} ) D. ( 29,504 mathrm{mi}^{3} ) | 9 |

139 | 58. Water flows in a tank 150 m x 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm, at the speed of 15 km per hour. In what time will the water be 3 metres deep ? (1) 100 hours (2) 120 hours (3) 140 hours (4) 150 hours | 9 |

140 | Find the total surface area of cubes having the following sides. ( mathbf{3} c boldsymbol{m} ) | 9 |

141 | If some coins each of diameter ( 1.5 mathrm{cm} ) and thickness ( 0.2 mathrm{cm} ) are melted and a right circular cylinder of height ( 10 mathrm{cm} ) and diameter ( 4.5 mathrm{cm} ) is made, then find the number of coins required to make the right circular cylinder A . 336 в. 450 c. 512 D. 545 | 10 |

142 | A cube with an edge length 4 is divided into 8 identical cubes. Calculate the difference between the combined surface area of the 8 smaller cubes and the surface area of the original cube. A . 48 B. 56 c. 96 D. 288 | 9 |

143 | The measures of a rectangular field are ( 20 mathrm{m} ) by ( 16 mathrm{m} . ) A cubical ditch of edge 4 ( mathrm{m} ) is dug at each of the four corners of the field and earth removed is spread uniformly over the remaining field. by what height does the field get raised? | 10 |

144 | Length of side of cube is ( 2 a ), then the length of diagonal is | 10 |

145 | Find the surface area of the hemisphere whose radius is ( 7 mathrm{cm} ) | 9 |

146 | A student has rectangular sheet of dimensions ( 14 mathrm{cm} times 22 mathrm{cm} . ) He wants to make a cylinder in such a way so that volume is minimum. Find the height of cylinder. | 9 |

147 | Suhail wants to paint the flour walls of a room having dimensions ( 20 m times 6 m ) From each can of paint, 96 sq. ( mathrm{m} ) of the area is painted. How many cans of paint will he need to paint the room? | 10 |

148 | Find the area of the cardboard required to make a closed box of length 250 ( mathrm{cm}, ) breath ( 0.5 mathrm{m} ) and height ( 15 mathrm{cm} ) | 9 |

149 | 59. The radius of the base ana height of a metallic solid cyl inder are r сm and 6 cm te spectively. It is melted and re cast into a solid cone of the same radius of base, The height of the cone is : (1) 54 cm (2) 27 cm (3) 18 cm (4) 9 cm | 10 |

150 | A hemispherical bowl is made up of stone whose thickness is ( 5 mathrm{cm} ). If the inner radius is ( 35 mathrm{cm}, ) find the total surface area of the bowl | 9 |

151 | How many spherical lead shots each ( 4.2 mathrm{cm} ) in diameter can be obtained from a rectangular solid (cuboid) of lead with dimensions ( left.66 c m, 42 c m, 21 c m . text { (Take } pi=frac{22}{7}right) ) A. 1500 B. 1200 c. 1300 D. 1600 | 9 |

152 | The volume of a solid cylinder is ( 448 pi mathrm{cm}^{3} ) and height ( 7 mathrm{cm} . ) Find its lateral surface area and total surface area. | 9 |

153 | The weight of a cubic meter of a certain metal is 480 kg. It is melted and then rolled into a square bar ( 4 m ) long. Now, an exact cube is cut from it. Find the weight of the cube A. ( 240 mathrm{kg} ) в. ( 80 mathrm{kg} ) c. ( 120 mathrm{kg} ) D. ( 60 mathrm{kg} ) | 10 |

154 | Praveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions ( 4 m times 3 m ? ) | 9 |

155 | If the circumference of the inner edge of a hemispherical bowl is ( frac{132}{7} mathrm{cm} ) then what is the capacity? A ( cdot 12 pi c m^{3} ) в. ( 18 pi c m^{3} ) ( mathbf{c} cdot 24 pi c m^{3} ) D. ( 36 pi c m^{3} ) | 9 |

156 | An ink container of cylindrical shape is filled with ink upto ( 91 % . ) Ball pen refills of length ( 12 mathrm{cm} ) and inner diameter 2 ( mathrm{mm} ) are filled upto ( 84 % ). If the height and radius of the ink container are 14 ( mathrm{cm} ) and ( 6 mathrm{cm} ) respectively, find the number of refills that can be filled with this ink. | 9 |

157 | 52. A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be (1) 1:2 (2) 2:1 (3) 1: 2 (4) 2:1 | 9 |

158 | Find the surface area of a sphere of radius: ( 10.5 mathrm{cm}left(text { in } c m^{2}right) ) | 9 |

159 | A hemispherical bowl made of wood has inner diameter of ( 10.5 mathrm{cm} ). Find the cost of painting it on the inside at the rate of Rs.12 per ( 100 mathrm{cm}^{2} ) | 9 |

160 | By melting down 3 spherical balls of radius ( 6 mathrm{cm}, 8 mathrm{cm} ) and ( 10 mathrm{cm} ) one big solid sphere is made. Calculate the radius of the new solid sphere. | 9 |

161 | The volumes of the two spheres are in the ratio ( 64: 27 . ) Find the ratio of their surface areas. ( mathbf{A} cdot 16: 9 ) B. 9: 16 c. 4: 3 D. 3: 4 | 9 |

162 | What is the ratio of volumes of spheres and hemisphere? A .2: 1 B. 4: 3 c. 2: 3 D. 1: 2 | 9 |

163 | A cylinder and ( a ) cone have equal bases. The height of the cylinder is ( 3 mathrm{cm} ) and the area of its base is ( 100 mathrm{cm}^{2} ). The cone is placed upon the cylinder. Volume of the solid figure so formed is ( 500 mathrm{cm}^{3} ) Find the total height (in ( c m ) ) of the figure. | 10 |

164 | The volume of a cylindrical toy is 628 ( c m^{3} . ) The radius of its base is ( 10 mathrm{cm} ) Find the height of the toy. ( (pi=3.14) ) | 9 |

165 | Seven spheres of equal radii are made by melting a silver-cuboid of dimensions ( 8 mathrm{cm} times times 11 mathrm{cm} times 9 mathrm{cm} . ) Find the radius of a silver sphere (in ( mathrm{cm} ) ). | 9 |

166 | A sphere of maximum volume is cut out from a solid hemisphere of radius r.The ratio of the volume of the hemisphere to that of the cut out sphere is: | 9 |

167 | How many spherical bullets can be made out of a cube of lead whose edge measures ( 22 mathrm{cm}, ) each bullet being ( 2 mathrm{cm} ) in diameter? A . 1347 B. 2541 ( c .2662 ) D. 5324 | 9 |

168 | The diameter of a sphere is ( 6 mathrm{cm} ). It is melted and drawn into a wire of water in the rise by ( 21 mathrm{cm} ? ) | 10 |

169 | A hemispherical bowl of radius unity is filled up with water upto the depth ( frac{1}{2} ) The volume of water in the bowl is A ( cdot frac{27 pi}{24} ) в. ( frac{5 pi}{24} ) c. ( frac{3 pi}{4} ) D. None of these | 9 |

170 | A solid cylinder of glass whose diameter is ( 1.5 mathrm{m} ) and height ( 1 mathrm{m} ) is melted and recasted into a sphere, then the radius of the sphere is ( A cdot 1 m ) B. ( 0.75 mathrm{m} ) c. ( 1.25 mathrm{m} ) D. ( 1.5 mathrm{m} ) | 9 |

171 | Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube. | 9 |

172 | Three cubes each of side ( 5 mathrm{cm} ) are joined end to end. Find the surface area of the resulting Cuboid A ( cdot 350 mathrm{cm}^{2} ) В. ( 300 mathrm{cm}^{2} ) ( mathrm{c} cdot 250 mathrm{cm}^{2} ) D. ( 200 mathrm{cm}^{2} ) | 9 |

173 | A solid cylinder of glass whose diameter is ( 1.5 m ) and height ( 1 m ) is melted and turned into a sphere. The diameter of ths sphere is- A. 1 metre B. 0.75 metre c. 1.25 metres D. 1.5 metres | 9 |

174 | A hemispherical tank is made up of an iron sheet ( 1 mathrm{cm} ) thick. If the inner radius is ( 1 mathrm{m} ), then find the volume of the iron used to make the tank. | 9 |

175 | The radius and height of an ice cream cone are in the ratio 4: 3 and area of its base is ( 154 mathrm{cm}^{2} ). Find its curved surface area. A ( cdot 192.5 mathrm{cm}^{3} ) В. ( 150 mathrm{cm}^{3} ) c. ( 176.3 mathrm{cm}^{3} ) D. ( 115.36 mathrm{cm}^{3} ) E . None of these | 9 |

176 | Find the length of edge of a cube with following surface area ( 1944 mathrm{cm}^{2} ) ( 2646 mathrm{cm}^{2} ) A. ( 28 mathrm{cm} ; 21 mathrm{cm} ) в. ( 17 mathrm{cm} ; 21 mathrm{cm} ) ( mathrm{c} .18 mathrm{cm} ; 21 mathrm{cm} ) D. ( 18 mathrm{cm} ; 20 mathrm{cm} ) | 9 |

177 | A right circular cylinder just encloses a sphere of radius ( r ). Find ratio of the area obtained in surface area of the sphere and curves surface area of the cylinder. | 9 |

178 | The volume of two spheres is in the ratio 64: 27 and the sum of their radiiis 7 cm. The difference in their total surface areas is ( mathbf{A} cdot 38 c m^{2} ) B. ( 58 c m^{2} ) ( mathbf{c} cdot 78 c m^{2} ) D. ( 88 mathrm{cm}^{2} ) | 9 |

179 | A solid having six equal square faces is called a A. Cube B. Cuboid c. Square D. Rectangle | 9 |

180 | If the diameter of the sphere is doubled, the surface area of the resultant sphere becomes ( x ) times that of the original one. Then, ( x ) would be A . 2 B. 3 ( c cdot 4 ) ( D ) | 9 |

181 | Find the radius of a sphere whose surface area is ( 154 mathrm{cm}^{2} ) | 9 |

182 | Which one of the following statement is INCORRECT? A. A cyclic parallelogram is a rectangle B. Set of points joining the middle points of all parallel chords of a circle constitute the longest chord of the circle C. Total surface area of a hemisphere is ( 2 pi r^{2} ) D. A fair coin is tossed The chance that it shows up head is 50% | 9 |

183 | A hemispherical bowl has inner diameter ( 11.2 mathrm{cm} . ) Find the volume of milk it can hold. | 9 |

184 | A cylinder has a diameter of ( 20 mathrm{cm} ). The area of curved surface is ( 1000 mathrm{cm}^{2} ) FindAthe height of the cylinder correct to one decimal place.The volume of the cylinder correct to one decimal place. (Take ( boldsymbol{pi}=mathbf{3 . 1 4}) ) | 9 |

185 | 51. The area of the iron sheet re- quired to prepare a cone 24 cm high with base radius 7 cm is (Take n = 22) (1) 408 cm (2) 708 cm2 (3) 804 cm2 (4) 704 cm2 | 9 |

186 | A solid spherical ball is prepared by melting a cone and cylinder having the same height and same base radius equal to ( r . ) Find the radius of the sphere. | 10 |

187 | The volume of sphere is ( frac{4}{3} pi c m^{3} . ) Then the radius is ( A ) B. 0.02 c. 0.01 D. 2 | 9 |

188 | The sum of length, breadth and depth of a cuboid is ( 19 mathrm{cm} ) and the length of its diagonal is ( 11 mathrm{cm} . ) Find the area of cuboid. | 9 |

189 | Find the surface area of a sphere of radius ( 1.4 mathrm{cm} .left(pi=frac{22}{7}right) ) | 9 |

190 | 55. The respective heights and vol- umes of a hemisphere and a right circular cylinder are equal, then the ratio of their radii is (1) 12 : 13 (2) 13 : 1 (3) 73 : 2 (4) 2: 13 | 9 |

191 | A well of diameter ( 3 m ) is dug 14 m deep. The earth taken out of it has been spread evenly all around it to a width of ( 4 m ) to form an embankment. Find the height of the embankment | 10 |

192 | A cylindrical vessel of height ( 24 mathrm{cm} ) and diamater ( 40 mathrm{cm} ) is full of water. Find the exact number of small cylindrical bottles, each of height ( 10 mathrm{cm} ) and diameter ( 8 mathrm{cm}, ) which can be filled with this water. | 9 |

193 | The radii of two cylinders are in the ratio 2: 3 and their heights are in the ratio ( 5: 3 . ) then what is the ratio of their volumes? A . 10: 17 B . 20: 27 c. 10: 27 D. 20: 37 | 9 |

194 | The diagram shows a box in the shape of a cube of lengths 2 m.The box is packed with cubes of lengths 1 cm.How many cubes does it hold? A. 8000 B. 8000000 c. 4000000 D. 40000 | 9 |

195 | Three solid cubes of sides ( 1 mathrm{cm}, 6 mathrm{cm} ) and ( 8 mathrm{cm} ) respectively are melted to form a new cube. Find the surface area of the cube so formed. A. 520 sq. ( mathrm{cm} ) B. 486 sq. ( mathrm{cm} ) c. 289 sq. ( mathrm{cm} ) D. 300 sq. ( mathrm{cm} ) | 9 |

196 | A solid metallic sphere of diameter ( 28 c m ) is melted and recast into a number of smaller cones, each of diameter ( 4 frac{2}{3} c m ) and height ( 3 c m . ) Find the number of cones so formed. | 10 |

197 | A brick whose length, breadth and height are ( 5 mathrm{m}, 6 mathrm{m}, ) and ( 7 mathrm{m} ) respectively. Find the surface area of the brick. A . 214 ( m^{2} ) B . 202 ( m^{2} ) c. ( 201 m^{2} ) D. 210 ( m^{2} ) | 9 |

198 | Find the volume of a hemisphere whose radius is ( frac{mathbf{3}}{mathbf{2}} boldsymbol{c m} ) | 9 |

199 | A building has 8 right cylindrical pillars whose cross sectional diameter is ( 1 mathrm{m} ) and whose height is ( 4.2 mathrm{m} ). Find the expenditure to paint these pillars at the rate of Rs.24 per ( boldsymbol{m}^{2} ) A . Rs.2534.40 B. Rs.2506.13 c. Rs.2610.9 D. Rs.2514.5 | 9 |

200 | A container shaped like a right circular cylinder having diameter ( 12 mathrm{cm} ) and height ( 15 mathrm{cm} ) is full of ice cream. The ice cream is to be filled into cones of height ( 12 mathrm{cm} ) and diameter ( 6 mathrm{cm}, ) having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. | 10 |

201 | A village with a population of 400 requires 150 I water per head per day. It has a tank measuring ( 20 mathrm{m} times 15 mathrm{m} times 6 ) ( mathrm{m} ) If the tank is full then how many days will the water last? A. 20 days B. 18 days c. 10 days D. 30 days | 10 |

202 | A solid cylinder of glass whose diameter is ( 1.5 mathrm{m} ) and height ( 1 mathrm{m} ) is melted an recasted into a sphere then the radius of the sphere is ( A cdot 1 m ) B. 0.75 ( m ) c. ( 1.25 mathrm{m} ) D. ( 1.5 mathrm{m} ) | 9 |

203 | The number of spherical lead shots each ( 4.2 mathrm{cm} ) in diameter that can be obtained from a rectangular solid with diameter ( 66 mathrm{cm} times 42 mathrm{cm} times 21 mathrm{cm} ) is A. 750 B. 3000 ( c cdot 1500 ) D. None of the above | 9 |

204 | A rectangle plot of land measures ( 45 mathrm{m} ) ( times 30 mathrm{m} . ) A boundary wall of height ( 2.4 mathrm{m} ) is built all round the plot at a distance of ( 1 mathrm{m} ) from the plot. Find the area of the inner surface of the boundary wall. A ( cdot 226.2 m^{2} ) В. ( 457.2 m^{2} ) D. ( 291.2 m^{2} ) | 9 |

205 | A cube of ( 4 mathrm{cm} ) has been painted on its surface in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red Two remaining surfaces have been left unpainted Now the cube is cut into smaller cubes of sides ( 1 mathrm{cm} ) each How many cubes will have at least blue | 10 |

206 | The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per ( mathrm{cm}^{3} ) ? | 9 |

207 | The surface area of a sphere is given by the formula A ( cdot 4 pi r^{2} ) в. ( 4 pi r ) ( mathrm{c} cdot 2 pi r^{2} ) D. ( frac{1}{2} pi r^{2} ) | 9 |

208 | Find a side of a cube whose total surface area is ( 486 mathrm{cm}^{2} ) | 9 |

209 | Say true or false. The volume of a sphere is equal to twothird of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. A. True B. False | 9 |

210 | If a wooden cylinder of radius ‘r’ and height ‘h’ is peeled to produce a perfect cone of same radius and height, then find the volume of the peels. | 9 |

211 | A cylindrical pencil of diameter ( 1.2 mathrm{cm} ) has one of its ends sharped into a conical shape of height ( 1.4 mathrm{cm} . ) The volume of the material removed is (in ( mathbf{A} cdot 4 cdot 224 ) B. 1.056 c. 10.56 D. 42.24 | 9 |

212 | A conical flask is full of water. The flask has base radius ( a ) and height ( 2 a ). The water is poured into a cylindrical flask of base-radius ( frac{2 a}{3} . ) Find the height of water in the cylindrical flask. A ( cdot frac{5}{2} a ) B. ( 2 a ) c. ( frac{3}{2} a ) D. 1a | 9 |

213 | Write the formula of curved & total surface areas of a hemisphere. Also find the ratio between then | 9 |

214 | The number of vertices in a cube is ( A cdot 6 ) B. 10 ( c cdot 8 ) D. 12 | 9 |

215 | If the volume of a right circular cylinder with its height equal to the radius is ( 25 frac{1}{7} c m,^{3}, ) then the radius of the cylinder is equal to A . ( pi ) B. 3 cm c. ( 4 c m ) D. ( 2 c m ) | 9 |

216 | If the diameter of the base and height of a cylinder are ( 6 mathrm{cm} ) and ( 14 mathrm{cm} ) respectively. Then find its volume. | 9 |

217 | Given that ( 1 mathrm{cu} . mathrm{cm} ) of marble weights 25 gms, the weight of a marble block 28 ( mathrm{cm} ) in width and ( 5 mathrm{cm} ) thick is ( 112 mathrm{kg} ) The length of the block is: A. ( 26.5 mathrm{cm} ) в. 32 ( mathrm{cm} ) c. ( 36 mathrm{cm} ) D. 37.5 cm | 10 |

218 | If the diagonal of cube is ( sqrt{300} mathrm{cms} ) then the surface area (in sq. cm) is A. 300 в. 600 ( c .1200 ) D. 2400 | 9 |

219 | There are 42 hemispherical bowls, each of radius ( 3.5 mathrm{cm} ). Find the quantity of water in litres which is just sufficient to fill these 42 bowls. (Take ( pi=frac{22}{7} ) ) A . 3.773 litres B. 3.553 litres c. 3.223 litres D. 4.773 litres | 9 |

220 | A toy is in the shape of cone mounted on hemisphere of same base radius. If the volume of the toy is ( 231 mathrm{cm}^{3} ) and its diameter is ( 7 mathrm{cm}, ) find the height of the toy. | 9 |

221 | In given figure of cube and cuboid, which one has a greater surface area? A. cube B. Cuboid c. cant compose D. None | 10 |

222 | A gulab jamun, contains sugar syrup up to about ( 30 % ) of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two, hemispherical ends with length ( 5 mathrm{cm} ) and diameter ( 2.8 mathrm{cm} ) | 10 |

223 | A hemispherical tank full of water is emptied by a pipe at the rate of 5 litres per second. How much time will it take to empty half of the tank, if it is ( 3.5 m ) in diameter? | 9 |

224 | A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 ( mathrm{cm} ) and its height is ( 15 mathrm{cm} . ) Find the cost of painting the toy at Rs.7 per ( 100 mathrm{cm}^{2} ) | 9 |

225 | If the error in the measurement of radius of a sphere is ( 2 % ) then the error in the determination of volume of the sphere will be – A . ( 8 % ) B. 2% ( c .4 % ) D. ( 6 % ) | 9 |

226 | Find the area of four walls of a room having length, breadth and height as 8 ( mathrm{m}, 5 mathrm{m} ) and ( 3 mathrm{m} ) respectively. Find the cost of white-washing the walls at the rate of Rs. ( 15 / m^{2} ) | 9 |

227 | The largest sphere is curved out of cube of side ( 14 c m ). Find surface area of sphere | 9 |

228 | A hemispherical container with radius ( 6 mathrm{cm} ) contains ( 325 mathrm{ml} ) of milk. Calculate the volume of milk that is needed to fill the container completely. ( (pi=3.142) ) A. ( 147.45 mathrm{ml} ) B. ( 127.45 mathrm{ml} ) c. ( 137.45 mathrm{ml} ) D. None | 9 |

229 | A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area in ( c m^{2} ) of the shape if the length of the shape be ( mathbf{7} boldsymbol{c m} ) | 9 |

230 | A metal pipe is ( 77 mathrm{cm} ) long. The inner diameter of a cross section is ( 4 mathrm{cm} ), the outer diameter being ( 4.4 mathrm{cm} . ) Find its inner curved surface area. | 9 |

231 | ( A 5 times 5 times 5 ) cube is formed by using1 ( x ) ( 1 times 1 ) cubes if we add another layer of ( operatorname{such} 1 times 1 times 1 ) cube in the ( 5 times 5 times 5 ) cube What will be the number of ( 1 times ) ( 1 times 1 ) cubes in the newly formed cube? A .216 в. 343 c. 294 D. 264 | 10 |

232 | The area of the floor of a room is ( 15 m^{2} .1 ) its height is ( 4 m ), then the volume of the air contained in the room is A. ( 60 d m^{3} ) в. ( 600 d m^{3} ) ( mathbf{c} cdot 6000 x m^{3} ) D. ( 60000 d m^{3} ) | 9 |

233 | Find the total volume of these three identical toy blocks | 10 |

234 | A wire is in the form of an equilateral triangle with area ( sqrt{3} m^{2} ). If it is changed into a circle, the radius will be: | 10 |

235 | If the radius of the sphere is increased by ( 100 % ), the volume of the corresponding sphere is increased by- ( mathbf{A} cdot 200 % ) B. ( 500 % ) c. ( 700 % ) D. ( 800 % ) | 9 |

236 | The dimensions of a cuboid are in the ratio of 1: 2: 3 and its total surface area is ( 88 m^{2} ). Find the dimensions of the cuboid. | 9 |

237 | If the sphere of radius ( 6 mathrm{cm} ) is melted and drawn into a wire of radius ( 0.02 mathrm{cm} ) then the length of the wire is: | 9 |

238 | A rectangular block of wood has dimensions ( 24 mathrm{cm} ) by ( 8 mathrm{cm} ) by ( 7 mathrm{cm} . ) It is cut up into children’s bricks. Each brick is a cube of side ( 3 mathrm{cm} ) Find the volume of wood that is left. | 10 |

239 | How many cuboids of size ( 4 c m times ) ( 3 c m times 1 c m 4 c m times 3 c m times 2 c m ) can be inscribed on cube of size ( 12 mathrm{cm} times ) ( 12 c m times 12 c m ? ) | 10 |

240 | A sphere is placed in an inverted hollow conical vessel of base radius ( 5 mathrm{cm} ) and vertical height ( 12 mathrm{cm} . ) If the highest point of the sphere is at the level of the base of the cone; find the radius of the sphere. Also find the ratio of the volume of the sphere to that of the cone. | 9 |

241 | Find the total surface area of a hemisphere of radius ( 3.5 mathrm{cm} ) | 9 |

242 | Evaluate ( int frac{boldsymbol{d} boldsymbol{x}}{sqrt{(boldsymbol{x}-boldsymbol{alpha})(boldsymbol{beta}-boldsymbol{x})}}, boldsymbol{beta}>boldsymbol{alpha} ) | 9 |

243 | A cylindrical vessel having diameter equal to its hight is fall of water which is poured into two identical cylindrical vessel with diameter ( 42 mathrm{cm} ) and height ( 21 mathrm{cm} ) which are filled compulsory. Find the cylindrical vessel | 9 |

244 | A cylindrical bucket, ( 32 mathrm{cm} ) high and with radius of base ( 18 mathrm{cm} ), is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is ( 24 mathrm{cm} . ) Find the radius and slant height of the heap. | 10 |

245 | A dairy produces a 500 -gram pack of butter in the shape of a cylinder. The radius of the circular end of the pack is ( 3.9 mathrm{cm} . ) and the length of the pack is 10.5 cm. The volume of the pack of the butter is ( x mathrm{cm}^{3} . ) The 500 gm pack is redesigned. It is now produced in the shape of a cuboid with a square end of side ( 6.5 mathrm{cm} . ) The length of the redesigned pack f butter is y cm. Now choose the correct options. This question has multiple correct options A. ( x=405 ) в. ( y=11.9 ) c. ( x=502 ) D. ( y=13.9 ) | 9 |

246 | Find the total surface area of a cuboid its length, breadth and height are ( 7 mathrm{cm} ) ( 5 mathrm{cm}, ) and ( 10 mathrm{cm} ) respectively. | 9 |

247 | The total surface area of a solid right circular cylinder is ( 231 mathrm{cm}^{2} ). Its curved surface area is two thirds of the total surface area. Find height of the cylinder. | 9 |

248 | Find the volume of a sphere whose radius is ( mathbf{0 . 6 3} boldsymbol{m} ) | 9 |

249 | A sphere is inscribed in a cubical box such that the sphere is tangent to all six faces of the box, What is the ratio of the volume of the cubical box to the volume of sphere? A . ( 6 pi ) в. ( 36 pi ) c. ( frac{4 pi}{3} ) D. ( frac{6}{pi} ) | 9 |

250 | If radius of a sphere is doubled, how many times its volume will be affected A. 2 times B. 4 times ( c .6 ) times D. 8 times | 9 |

251 | The sum of the length, breadth and height of a cuboid is ( 38 mathrm{cm} ) the length of its diagonal is ( 22 mathrm{cm} . ) Find the surface area of the cuboid. | 9 |

252 | 72. The height of a right prism with a square base is 15 cm. If the area of the total surfac- es of the prism is 608 sq. cm, its volume is (1) 910 cm3 (2) 920 cm3 (3) 960 cm3 (4) 980 cm3 | 10 |

253 | Find the total surface area of a hollow cylinder of internal radius ( 3 mathrm{cm} ) thickness ( 1 mathrm{cm} ) and height ( 14 mathrm{cm} ) ( A cdot 330 mathrm{cm}^{3} ) B. ( 660 mathrm{cm}^{2} ) c. ( 990 mathrm{cm}^{2} ) D. ( 1320 mathrm{cm}^{2} ) | 9 |

254 | A gas cylinder has a diameter of ( 14 mathrm{m} ) and height is ( 0.2 mathrm{m} ). Find its surface area. ( (pi=22 / 7) ) A. ( 316.512 m m^{2} ) B. ( 316.512 m ) ( mathbf{c} cdot 316.512 m^{3} ) D. ( 316.512 m^{2} ) | 9 |

255 | The radius of a sphere of lead is ( 8 mathrm{cm} ) The number of spheres of radius ( 5 mathrm{mm} ) made by melting it will be A. 6000 approx B. Greater than 4000 and less than 5000 c. Greater than 3000 and less than 4000 D. Less than 3000 | 9 |

256 | The number of solid spheres, each of diametres ( 6 mathrm{cm}, ) that could be moulded to form a solid metal cylinder of height ( 45 mathrm{cm} ) and diameter ( 4 mathrm{cm} ) is ( A cdot 3 ) B. 4 ( c .5 ) ( D ) | 9 |

257 | A water tank is ( 1.4 mathrm{m} ) long. Im wide and 0.7m deep. then the volume of the tank in litres A. 780 litres B. 860 litres c. 980 litres D. none of these | 9 |

258 | A solid sphere of diameter ( 12 mathrm{cm} ) is melted and draw into a wire of radius ( mathbf{1} ) ( frac{1}{5} c m ) then the length of the wire is A . ( 108 mathrm{m} ) в. 72 ( mathrm{m} ) ( c cdot 84 m ) D. None | 9 |

259 | How many bricks, each measuring ( 25 c m times 12.5 c m times 7.5 c m ) will be needed to construct a wall ( 15 mathrm{m} ) long, 1.8 ( m ) high and ( 37.5 mathrm{cm} ) thick? A. 4400 B. 4660 ( c .4320 ) D. 4575 | 10 |

260 | An open box is made of 3cm thick. Its external length, breadth, and hights are ( 1.48 mathrm{m}, 1.16 mathrm{m}, 8.3 mathrm{dm} . ) Find the cost of painting the inner surface at 50 p per ( 100 mathrm{cm}^{2} ) | 9 |

261 | Say true or false. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1: 2: 3 A. True B. False | 9 |

262 | Choose the correct answers from the alternatives given. If a cone, a hemisphere and a cylinder stand on the same base and have | 10 |

263 | The surface area of a cube of side is ( 27 mathrm{cm} ) is: ( mathbf{A} cdot 2916 mathrm{cm}^{2} ) В. ( 729 mathrm{cm}^{2} ) ( mathbf{c} cdot 4374 c m^{2} ) D. ( 19683 c m^{2} ) | 9 |

264 | 66. If the height of a given cone be doubled and radius of the base remains the same, the ratio of the volume of the given cone to that of the second cone will be (1) 2:1 (2) 1:8 (3) 1:2 (4) 8:1 | 9 |

265 | A sphere of diameter ( 12.6 mathrm{cm} ) is melted and cast into a right circular cone of height ( 25.2 mathrm{cm} . ) The diameter of the base of the cone is? A ( .158 .76 mathrm{cm} ) B . ( 79.38 mathrm{cm} ) c. ( 12.6 mathrm{cm} ) D. ( 69.39 mathrm{cm} ) | 9 |

266 | A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are ( 6 mathrm{cm} ) and ( 4 mathrm{cm} ) respectively. Find the height of water in the cylinder(in cm). | 9 |

267 | Find the total surface area of cubes having the following sides. ( 6.8 m ) | 9 |

268 | How many ions ( 1.75 mathrm{cm} ) in diameter and 2 mm thick must be melted to form a cuboid ( 11 mathrm{cm} times 10 mathrm{cm} times 7 mathrm{cm} ? ) | 10 |

269 | The length, breadth and height of a cuboid are in the ratio 4: 2: 1 and its total surface area is ( 1372 m^{2} ). Find the dimensions of the cuboid. | 9 |

270 | Calculate the volume of a cylinder where the area of a base is ( 40 mathrm{mm}^{2} ) and height is ( 4.5 mathrm{mm} ) A ( cdot 180 mathrm{cm}^{3} ) В. ( 181 mathrm{mm}^{3} ) ( mathbf{c} cdot 180 m m^{3} ) D. ( 180.4 mathrm{mm}^{3} ) | 9 |

271 | If the surface area of a hemisphere is ‘S then express ‘ ( r^{prime} ) in terms of ‘ ( S ) ‘. | 9 |

272 | 3 of the volume of a right circu- lar cone whose height is 21 cm and radius of the base is the ra- dius of the circle of area 154 cm, is (1) 727 cm (2) 627 cm 13 818 cm (4) 718 cm | 9 |

273 | A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface. The radius is decreasing at a constant rate. A. True B. False | 9 |

274 | The dimensions of a rectangular box are in the ratio 1: 2: 4 and the difference between the costs of covering it with the cloth and sheet at the rate of ( R s .20 ) and Rs.20.50 per square metre, respectively is ( R s .126 . ) Find the dimensions of the box A. ( 4 c m, 7 c m ) and ( 10 c m ) B. ( 2 c m, 4 c m ) and ( 11 c m ) c. ( 3 c m, 6 c m ) and ( 12 c m ) D. ( 7 c m, 8 c m ) and ( 13 c m ) | 9 |

275 | If the radius and the height of a right circular cylinder are doubled, its volume becomes A. 2 times B. 3 times c. 4 times D. 8 times | 9 |

276 | The difference between the outer and the inner curved surface areas of an open cylinder is ( 88 mathrm{cm}^{2} ). If its length is ( 14 mathrm{cm} ) and volume of the material in it is ( 176 mathrm{cm}^{3}, ) find the inner diameter of the cylinder. A. ( 3 mathrm{cm} ) в. ( 4 mathrm{cm} ) ( c cdot 2 mathrm{cm} ) D. ( 1 mathrm{cm} ) | 9 |

277 | The volume of a largest sphere that can be cut from cylindrical log of wood of base radius ( 1 m ) and height ( 4 m ) is: A ( cdot frac{8}{3} pi m^{3} ) в. ( frac{10}{3} pi m^{3} ) c. ( frac{16}{3} pi m^{3} ) D. ( frac{4}{3} pi m^{3} ) | 9 |

278 | A metallic sphere ( 1 mathrm{cm} ) in diameter is beaten into a circular sheet of uniform thickness equal to 1 mm. Find the radius of the sheet | 10 |

279 | Find the surface area of a sphere of diameter: ( mathbf{3 . 5} mathrm{cm} ) | 9 |

280 | AS. A spherical lead ball of radius 10cm is melted and small lead balls of radius 5mm are made. The total number of possible small lead balls is (Take it = 22 7) (1) 8000 (3) 800 (2) 400 (4) 125 | 10 |

281 | Find the surface area of a sphere of radius ( 21 mathrm{cm} ) | 9 |

282 | A cylindrical tennis ball container can contain maximum three ball stacked on one another. The top and bottom balls also touch the lid and the base of the base of the container respectively. If the volume of a tennis ball is ( 240 mathrm{cm}^{3} ), then what is the volume of the container? A ( cdot 1080 mathrm{cm}^{3} ) B. ( 840 mathrm{cm}^{3} ) c. ( 1440 mathrm{cm}^{3} ) D. ( 720 mathrm{cm}^{3} ) | 9 |

283 | if the total surface area of a solid hemisphere is ( 462 mathrm{cm}^{2} ) find its volume | 9 |

284 | Find the volume of the sphere whose curved surface area is ( 616 mathrm{cm}^{2} ) | 9 |

285 | If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere? A . 1: 8 B. 1: 4 ( mathbf{c} cdot 1: 27 ) D. 8: 1 | 9 |

286 | Find the total surface area of a cube with side ( 5 mathrm{cm} ) | 9 |

287 | Find the volume of largest sphere covered out of a cube of side ( 7 mathrm{cm} ) | 10 |

288 | If the height of cylinder increases from 8 inches to 12 inches, then its volume increases from ( 72 pi ) to ( V ). Find the value of ( boldsymbol{V} ) ( mathbf{A} cdot 76 pi ) в. ( 108 pi ) ( c .328 pi ) D. ( 576 pi ) | 9 |

289 | The circumference of the base of a cylindrical vessel is ( 132 mathrm{cm} ) and its height is 25 cm. How many litres of water can it hold? ( left(1000 mathrm{cm}^{3}=1 lright) ) | 9 |

290 | Find the volume of sphere whose radius is ( 3 mathrm{cm} ) | 9 |

291 | Each of the cubes is ( 1 mathrm{m} ) in length. The total surface area of the cuboid is ( mathbf{A} cdot 86 m^{2} ) B. ( 85 m^{2} ) ( mathbf{c} cdot 84 m^{2} ) D. ( 80 m^{2} ) | 9 |

292 | The surface area of a cube whose volume is ( 343 m^{3} ) is ( mathrm{K} mathrm{cm}^{2} ) the value of ( mathrm{K} ) is A . 180 B. 364 ( c cdot 294 ) D. 394 | 9 |

293 | A box is 1 m long, ( 60 mathrm{cm} ) wide and ( 40 mathrm{cm} ) high. Find the expenditure of colouring its all outer side without its bottom at the rate of ( R s .20 ) per square meter. | 9 |

294 | The radius of a sphere is ( 9 mathrm{cm} ) lt is melted and drawn into a wire of diameter 2 mm Find the lenght of the wire in meters A . 972 B. 792 ( c cdot 292 ) D. 97.2 | 9 |

295 | A sphere of radius ( r ) lies inside a cube and touches each of the six sides of the cube. Calculate the volume of the cube in terms of ( r ) A ( cdot r^{3} ) B ( .2 r^{3} ) ( c cdot 4 r^{3} ) D. ( frac{4}{3} pi r^{3} ) E ( .8 r^{3} ) | 10 |

296 | An ice cream cone is the union of a right circular cone and a hemisphere that has the same circular base as the cone. Find the volume of the ice cream, if the height of the cone is ( 9 mathrm{cm} ) and the radius of its base is ( 2.5 mathrm{cm} ) | 9 |

297 | Find the mass of 200 steel spherical ball bearings, each of which has radius ( 0.7 mathrm{cm}, ) given that the density of steel is ( 7.95 g / c m^{3} .(text { Mass }=text { Volume } times text { Density }) ) A . ( 2.29 mathrm{Kg} ) в. ( 2.9 mathrm{Kg} ) ( mathrm{c} .3 .29 mathrm{Kg} ) D. None of these | 9 |

298 | A sphere and a cube have the same surface area. Find out the ratio of the volume of sphere to that to the cube. A. ( 6: pi ) B . ( sqrt{6}: sqrt{pi} ) c. ( sqrt{6}: pi ) D. ( 6: sqrt{pi} ) | 10 |

299 | Liquid kerosene fills a conical vessel of base radius ( 2 mathrm{cm} ). and height ( 3 mathrm{cm} . ) This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius ( 2 mathrm{cm} . ) The total height of kerosene after all of it is collected in the cylindrical jar is – ( mathbf{A} cdot pi mathrm{cm} ) B. ( 2 pi mathrm{cm} ) ( c cdot 1 mathrm{cm} ) ( D cdot 2 mathrm{cm} ) | 10 |

300 | The volume of cylinder if the base area is ( 20 c m^{2} ) and height is ( 5 c m ) | 9 |

301 | Find the total cost of white washing the 4 walls of a cuboidal room at the rate Rs.15 per ( m^{2} . ) The internal measures of the cuboidal room are length ( 10 mathrm{m} ) breadth ( 4 mathrm{m} ) and height ( 4 mathrm{m} ) | 9 |

302 | Eight spheres of same radius from a metallic sphere of ( 10 mathrm{cm} ) radius, are formed. Find the surface area of each sphere so obtained. | 9 |

303 | Calculate the surface area of a sphere with radius ( 3.2 mathrm{cm} ) A ( cdot 110.6 mathrm{cm}^{2} ) B . ( 128.6 mathrm{cm}^{2} ) c. ( 131.5 mathrm{cm}^{2} ) D. None of these | 9 |

304 | The dimensions of a room are ( 10 mathrm{m} times 7 ) ( mathrm{m} times 5 mathrm{m} . ) There are 2 doors and 3 windows in the room. The dimensions of the doors are ( 1 mathrm{m} times 3 mathrm{m} ). One window is of the size ( 2 mathrm{m} times 1.5 mathrm{m} ) and other two windows are size ( 1 mathrm{m} times 1.5 mathrm{m} ). The cost of painting the walls at Rs. 3 per ( m^{2} ) is A. Rs. 474.00 B. Rs. 578.00 c. Rs. 648.00 D. Rs. 849.00 | 10 |

305 | The height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is? A ( cdot frac{2 R}{3} ) в. ( frac{R}{3} ) c. ( frac{2 R}{sqrt{3}} ) D. ( frac{R}{sqrt{3}} ) | 9 |

306 | A sphere of diameter ( 6 mathrm{cm} ) is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is ( 12 mathrm{cm} ). If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel? | 9 |

307 | STATEMENT – 1: The volume of largest sphere that can be carved out from cube of side a cm is ( frac{1}{6} pi a^{3} ) STATEMENT – 2: Volume of sphere is ( frac{4}{3} pi r^{3} ) and for largest sphere to carved from cube radius of sphere ( = ) side of | 9 |

308 | 27 metal balls each of radius r are melted together to form one big sphere of radius R. Then the ratio of surface area of the big sphere to that of a ball is A . 9: 1 B. 3: 2 c. ( sqrt{27}: sqrt{5} ) D. ( sqrt{3}: 1 ) | 9 |

309 | A hemispherical tank full of water is emptied by a pipe at the rate of ( 3 frac{4}{7} ) litres per second. How much time will it take to make the tank half-empty, if the tank is ( 4 m ) in diameter | 9 |

310 | Metal spheres, each of radius ( 2 mathrm{cm}, ) are packed into a rectangular box of internal dimensions ( 16 mathrm{cm} times 8 mathrm{cm} times 8 ) cm. When 16 spheres are packed the box filled with preservative liquid. Find the volume of this liquid. (Give the answer to the nearest integer value) ( mathbf{A} cdot 482 c m^{3} ) В. ( 478 mathrm{cm}^{3} ) ( mathrm{c} cdot 488 mathrm{cm}^{3} ) D. ( 490 mathrm{cm}^{3} ) | 9 |

311 | A sphere of diameter ( 10 mathrm{cm} ) weighs 44 kg. The weight of a sphere of the same material whose diameter is ( 6 mathrm{cm} ) is A . ( 2.64 mathrm{kg} ) в. ( 1.584 mathrm{kg} ) c. ( 0.9504 mathrm{kg} ) D. ( frac{4}{3}(0.9504) k g ) | 9 |

312 | A sphere of radius ( r, ) inside a cube touches each one of the six sides of the cube. What is the volume of the cube in terms of ( r ? ) ( mathbf{A} cdot 8 r^{3} ) B ( .2 r^{3} ) ( mathbf{c} cdot 4 r^{3} ) D. ( frac{4}{3} pi r ) | 9 |

313 | The area of three adjacent faces of a cuboid are ( x, y ) abd ( z . ) If the volume is ( V ) prove that ( V^{2}=x y z ) | 9 |

314 | If the volume and surface area of a sphere are numerically the same, then its diameter is A. 6 units B. 8 units c. 10 units D. 12 units | 9 |

315 | Water in a canal, ( 30 d m ) wide and ( 12 d m ) deep, is flowing with a speed of 10 ( k m / ) hour. How much area will it irrigate in 30 minutes, if 8 cm of standing water is required for irrigation A ( cdot 220500 m^{2} ) B . ( 22500 m^{2} ) c. ( 220000 m^{2} ) D. 225000 ( m^{2} ) | 9 |

316 | A cuboid with equal length, breadth and height is called a | 10 |

317 | Water flows at the rate of ( 10 mathrm{m} ) per min from cylindrical pipe ( 5 mathrm{mm} ) in diameter How long will it take to fill up a conical vessel whose diameter at the base is 40 ( mathrm{cm} ) and depth ( 24 mathrm{cm} ? ) A. 48 min 15 sec B. 51 min 12 sec c. 52 min 1 sec D. 55 min | 10 |

318 | A cone, hemisphere and a cylinder stand on the same base and have equal height. Find the ratio of their: Volumes. | 10 |

319 | 55. The respective heights and vol- umes of a hemisphere and a right circular cylinder are equal, then the ratio of their radii is (1) (2 : 13 (2) T3 : 1 (3) 3 : 2 (4) 2: 13 | 9 |

320 | 59. A conical flask is full of water. The flask has base radius r and height h. This water is poured into a cylindrical flask of base radius mr. The height of water in the cylindrical flask is 2h (1) 2h (3) 2h (2) , m? 19h m | 10 |

321 | Diameter of a sphere is ( 28 mathrm{cm} ). Find its surface area(in ( left.c m^{2}right) ) | 9 |

322 | The surface area of a cube is ( 600 mathrm{cm}^{2} ) Find its volume A ( cdot 1000 mathrm{cm}^{3} ) в. ( 729 mathrm{cm}^{3} ) ( c cdot 512 c m^{3} ) D. None of these | 10 |

323 | The diagram shows the cross section of six identical marbles touching each other on a horizontal surface. f the volume of a mabrle is ( frac{9 pi}{2} c m^{3} ) calculate the length of ( mathrm{PQ} ), in ( mathrm{cm} ). ( A ) в. 2 ( c cdot 18 ) 0.22 | 9 |

324 | The outer length, breadth and height of a wooden box open at the top are ( 10 mathrm{cm} ) ( 8 mathrm{cm} ) and ( 5 mathrm{cm} ) respectively. If the thickness of the wood is ( 1 mathrm{cm} ), the total surface area of the box is A ( cdot 420 mathrm{cm}^{2} ) В. ( 452 mathrm{cm}^{2} ) ( mathrm{c} cdot 451 mathrm{cm}^{2} ) D. ( 483 mathrm{cm}^{2} ) | 9 |

325 | A spherical ball of lead ( 3 mathrm{cm} ) in diameter is melted and recast into three spherical balls. If the diameter of two balls be ( frac{3}{2} mathrm{cm} ) and ( 2 mathrm{cm}, ) find the diameter of the third ball. | 9 |

326 | If a sphere and a cube have the same volume then the ratio of the surface of the sphere to that of the cube is A ( cdot sqrt{6}: sqrt{pi} ) B. ( sqrt[3]{3 pi}: sqrt[3]{3} ) C ( cdot sqrt[3]{pi}: sqrt[3]{6} ) D. none of these | 9 |

327 | A cylindrical rod of iron whose height is four times its radius is melted and cast into the spherical balls of the same radius then the number of balls is ( A cdot 2 ) B. 3 ( c cdot 4 ) D. | 9 |

328 | If a solid metallic sphere of radius ( 8 mathrm{cm} ) is melted and recasted into ( n ) spherical solid balls of radius ( 1 mathrm{cm}, ) then ( n ) is: A . 500 в. 510 c. 512 D. 516 | 9 |

329 | The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius ( 1 mathrm{cm} ) and height 5 ( mathrm{cm} ) is : A ( cdot frac{4}{3} pi ) в. ( frac{10}{3} pi ) c. ( 5 pi ) D. ( frac{20}{3} pi ) | 9 |

330 | Find the volume and surface area of a sphere of radius ( 6.3 mathrm{cm} ) | 9 |

331 | A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is ( 14 mathrm{cm} ) and the total height of the vessel is ( 13 mathrm{cm} ). Find the inner surface area of the vessel. | 10 |

332 | If the surface area of a sphere is ( 324 pi c m^{2} ) then its volume is ( mathbf{A} cdot 950 pi mathrm{cm}^{3} ) В. ( 972 pi mathrm{cm}^{3} ) ( mathbf{c} cdot 975 pi mathrm{cm}^{3} ) D. ( 980 pi mathrm{cm}^{3} ) | 9 |

333 | Find the volume and surface area of a sphere of radius ( 8.4 mathrm{cm} .left(pi=frac{22}{7}right) ) | 9 |

334 | If the radius of a sphere is doubled, what will be the ratio of its surface area and volume as to that of the first sphere A. 7: 1,8: 1 B. 5: 1,8: 1 c. 3: 1,8: 1 D. 4: 1,8: 1 | 9 |

335 | A circus tent is cylindrical to a height of ( 4 mathrm{m} ) and conical above it If its diameter is ( 105 mathrm{m} ) and the slant height of the cone is ( 80 mathrm{m} ) then the total surface area of the canvas required is A. ( 15540 m^{2} ) В. ( 30880 m^{2} ) c. ( 46020 m^{2} ) D. ( 14520 m^{2} ) | 9 |

336 | A rectangular room of the dimension ( 8 m times 6 m times 3 m ) is to be painted. If it ( operatorname{costs} ) Rs.60 per square metre, find the ( operatorname{cost} ) of painting the walls of the room. | 9 |

337 | Find the L.S.A of a cuboid whose dimensions are given by ( 3 m times 5 m times ) ( 4 m ) | 9 |

338 | The largest sphere is carved out of a cube of a side ( 7 mathrm{cm} . ) Find the volume of the sphere. | 9 |

339 | Find the surface area of a sphere of diameter: ( 21 mathrm{cm} ) | 9 |

340 | Three cuboids of width ( 8 mathrm{m} ) and joined along its width. Find surface area of resulting cuboid. ( (l=1 mathbf{m}, h=1 mathbf{m}) ) ( mathbf{A} cdot 34 m^{2} ) B. ( 64 m^{2} ) ( mathbf{c} cdot 98 m^{2} ) D. None of the above | 9 |

341 | What is the surface area of a cube whose volume is ( 64 mathrm{cm}^{3} ) ? ( mathbf{A} cdot 16 mathrm{cm}^{2} ) B. ( 64 mathrm{cm}^{2} ) c. ( 96 mathrm{cm}^{2} ) D. ( 128 mathrm{cm}^{2} ) | 9 |

342 | The surface area of a sphere is ( 616 mathrm{cm}^{2} ) What is its volume? ( left[boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) A. ( 1277.33 mathrm{cm}^{3} ) В. ( 1437.33 mathrm{cm}^{3} ) c. ( 1627.33 mathrm{cm}^{3} ) D. ( 1337.33 mathrm{cm}^{3} ) | 9 |

343 | Find the amount of water displaced by a solid spherical ball of diameter ( 4.2 mathrm{cm} ) when it is completely immersed in water | 9 |

344 | A right circular cone and a right circular cylinder have equal base and equal height. If radius of the base and the height, are in the ratio ( 5: 12, ) then ratio of the total surface area of the cylinder to that of the cone is A . 3: B. 13: c. 17: 9 D. 34: | 9 |

345 | The volume of hollow sphere is A ( cdot frac{4}{3} pi quadleft(R^{3}-r^{3}right) c m^{3} ) B・frac{2 } { 3 } pi ( quadleft(R^{3}-r^{3}right) c m^{3} ) ( mathbf{c} cdot frac{1}{2} pi quadleft(R^{3}-r^{3}right) c m^{3} ) | 9 |

346 | Find the volume of a sphere whose radius is (i) ( 7 mathrm{cm} ) (ii) ( 0.63 m ) | 9 |

347 | The radius of a wire is decreased to one- third and its volume remains the same. The new length is how many times the original length? A. 1 time B. 3 times ( c .6 ) times D. 9 times | 9 |

348 | Find the volume of a hemisphere of radius 7 dm. A ( cdot 708.67 d m^{3} ) B . ( 818.67 d m^{3} ) c. ( 717.67 d m^{3} ) D. ( 718.67 d m^{3} ) | 9 |

349 | The total surface area of a solid hemisphere is ( 462 mathrm{cm}^{2} . ) Find its radius. | 9 |

350 | A cylindrical vessel ( 60 mathrm{cm} ) in diameter is partially filled with water. A sphere, ( 54 mathrm{cm} ) in diameter is gently dropped into the vessel. To what further height will water rise in the cylinder? A ( .20 .02 mathrm{cm} ) B . ( 30.29 mathrm{cm} ) c. ( 29.16 mathrm{cm} ) D. ( 25 mathrm{cm} ) | 9 |

351 | 58. The base of a right pyramid is an equilateral triangle of side 4 cm. The height of the pyramid is half of its slant height. Its vol- ume is cm3 | 10 |

352 | The radius of a sphere is ( 3.5 mathrm{cm} ). Find the surface area and volume. | 9 |

353 | A spherical ball of lead ( 5 mathrm{cm} ) in diameter is melted and recast into three spherical balls. The diameters of two of these balls are ( 2 mathrm{cm} ) and ( 2(14.5)^{1 / 3} mathrm{cm} ) Find the diameter of the third ball. A. ( 8 mathrm{cm} ) B. ( 5 mathrm{cm} ) ( c .4 mathrm{cm} ) D. ( 1 mathrm{cm} ) | 10 |

354 | Find the edge of a cube whose volume is 216 cubic centimetres. | 9 |

355 | Calculate the volume of the hemisphere. A. ( 1095.23 mathrm{cm}^{3} ) B . ( 2095.23 mathrm{cm}^{3} ) c. ( 3095.23 mathrm{cm}^{3} ) D. ( 4095.23 mathrm{cm}^{3} ) | 9 |

356 | A cubical box has each edge ( 10 mathrm{cm} ) and another cuboidal box is ( 12.5 mathrm{cm} ) long, 10 cm wide and ( 8 mathrm{cm} ) high. i) Which box has the greater lateral surface area and by how much? ii) Which box has the smaller total surface area and by how much? | 9 |

357 | From a solid circular cylinder with height ( 10 c m ) and radius of the base ( 6 c m, ) a right circular cone of the same height and same base is removed. Find the volume of the remaining solid. Also, find the whole surface area. | 10 |

358 | The volume of a hemisphere is ( 2425 frac{1}{2} c m^{3} . ) Find its curved surface area. ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) | 9 |

359 | 56. If the length of the diagonal of a cube is 8/3 cm, then its surface area is (1) 192 cm (2) 512 cm (3) 768 cm2 (4) 384 cm2 | 10 |

360 | Find the volume of a hemisphere of radius ( 6.3 mathrm{cm}(pi=22 / 7) ) A ( .523 .9 mathrm{cm}^{3} ) B . ( 520.91 mathrm{cm}^{3} ) D. ( 510.91 mathrm{cm}^{3} ) | 9 |

361 | The volume of a cubic is ( 1000 mathrm{cm}^{3} ). Find its total surface area- – A. ( 400 mathrm{cm}^{2} ) B. ( 600 mathrm{cm}^{2} ) c. ( 200 mathrm{cm}^{2} ) D. None of these | 9 |

362 | A hemispherical bowl of internal radius ( 9 mathrm{cm} ) is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius ( 1.5 mathrm{cm} ) and height ( 4 mathrm{cm} ) How many bottles are needed to empty the bowl? | 9 |

363 | Jabu is building a new flower bed and is using a bucket to carry soil from another part of the garden to the new bed. He knows his bucket has a capacity of 10 litres. If he has 300 litres of soil, and for each trip he fills the bucket to the top, how many trips will Jabu have to make with bucket? A . 10 B . 20 c. 30 D. 40 | 9 |

364 | A hemispherical bowl has diameter 9 cm. The liquid is poured into cylindrical bottles of diameter ( 3 mathrm{cm} ) and height 3 cm. If a full bowl of liquid is filled in the bottles, find how many bottles are required. | 9 |

365 | How does the total surface area of a box change if Each dimension is doubled? Express in words. Can you find the area if each dimension is multiplied ( n ) times? | 9 |

366 | A wooden toy in the form of cone surmounted on a hemisphere. The diameter of the base of the cone is ( 6 mathrm{cm} ) and height is ( 4 mathrm{cm} ). find the cost of painting the toy at the rate of ( R s .5 ) per ( 1000 mathrm{cm}^{2} ) | 9 |

367 | The radii of two cylinders are in the ratio 2: 3 and their heights are in the ratio ( mathbf{5}: mathbf{3}, ) then the ratio of their volumes is ( ? ) A . 15: 16 B. 14: 17 c. 20: 27 D. 4: 9 | 9 |

368 | A hemisphere of lead of radius ( 7 mathrm{cm} ) is cast into a right circular cone of height ( 49 mathrm{cm} . ) Find the radius of the base in ( mathrm{cm} ) | 9 |

369 | A plastic box ( 1.5 mathrm{m} ) long, ( 1.25 mathrm{m} ) wide, and ( 65 mathrm{cm} ) deep is to be made. It is to be opened at the top. Ignoring the thickness of the plastic, the cost of the sheet for covering it, if a sheet measuring ( 1 m^{2} ) costs Rs. 20 is: A . Rs. 100 B. Rs. 109 c. Rs. 115 D. Rs. 110 | 9 |

370 | A toy is in the form of a cone of radius ( 3.5 mathrm{cm} ) mounted on a hemisphere of same radius. The total height of the toy is ( 15.5 mathrm{cm} . ) Find the total surface area of the toy. | 10 |

371 | A company makes a metallic block having square bases with volume 640 ( c m^{3}, ) and height ( 10 mathrm{cm} . ) If Robin wants to paint the block with the paints at the rate of Rs 15 per ( c m^{2} ), then find the cost of painting Robin has to pay. A . Rs 5680 B. Rs 6595 c. Rs 6720 D. Rs 6690 | 9 |

372 | The radius of a wooden hemisphere is 10 cm. What is its volume? If this hemisphere is curved into a cone | 10 |

373 | The diameter of base of a cylinder is ( 14 mathrm{cm} ) and its height is ( 20 mathrm{cm} . ) Find the whole surface area and volume. | 9 |

374 | A solid right circular wax cone of height ( 12 mathrm{cm} ) and radius ( 4 mathrm{cm} ) is melted and smaller wax cones of height ( 4 mathrm{cm} ) and radius ( 2 mathrm{cm} ) are made The number of smaller cones will be ( A cdot 48 ) B. 18 ( c cdot 24 ) D. 36 | 9 |

375 | Find the lateral or curved surface area of a closed cylindrical petrol storage tank that is ( 4.2 m ) in diameter and ( 4.5 m ) high. | 9 |

376 | Find the ratio of the edge of a cube to the radius of a sphere, if the volume of the cube is equal to the volume of the sphere A . 1.61 в. 2.05 c. 2.33 D. 2.45 E . 2.65 | 9 |

377 | Water flows through a cylindrical pipe of internal diameter ( 7 mathrm{cm} ) at ( 5 mathrm{m} / mathrm{s} ) Calculate: (i) the volume, in litres, of water discharged by the pipe in 1 minute (ii) the time, in minutes, the pipe would take to fill an empty rectangular tank ( 4 m ) by ( 3 m ) by ( 2.31 m ) | 9 |

378 | There is a right circular cone of height ( h ) and vertical angle ( 60^{circ} . ) A sphere when placed inside the cone, it touches the curved surface and the base of the cone. The volume of sphere is A ( cdot frac{4}{3} pi h^{3} ) В ( cdot frac{4}{9} pi h^{3} ) c. ( frac{4}{27} pi h^{3} ) D. ( frac{4}{81} pi h^{3} ) | 9 |

379 | If the circumference of the base of a cylinder is ( 44 c m ) and height ( 20 c m ), then its lateral surface area is A. 440 sq.cm B. 880 sq.cm c. ( 88 s q . c m ) D. 44 sq.cm | 9 |

380 | If the side of cube is ( 2 mathrm{m} ), then surface area of cube is ( mathbf{A} cdot 24 m^{2} ) B. ( 124 mathrm{m}^{2} ) ( c cdot 24 m ) D. ( 124 mathrm{m} ) | 9 |

381 | A cylinder has hemispherical ends having radius ( 7 mathrm{cm} ) and total height of solid is ( 104 mathrm{cm} ). If its outer surface is to be polished and cost of polish is rs 100 per.sq.mtr find the total cost of polish. | 9 |

382 | The radius of a sphere increased by 50 percent. By how many per cent did the surface area of the sphere increase? | 9 |

383 | A cylinder of radius ( 12 mathrm{cm} ) contains water upto the height of ( 20 mathrm{cm} . A ) spherical iron ball is dropped into the cylinder and thus water level is raised by ( 6.75 mathrm{cm} ) what is the radius of the ball? | 9 |

384 | 56. Base of a right pyramid is a square. The length of a diagonal of the base is 122 cm. If each lateral surface of the pyramid is a equilateral triangle, then its vol- ume (in cu. cm) is (1) 208/2 (2) 288/2 (3) 288 (4) 28873 | 10 |

385 | Bricks measuring ( 40 mathrm{cm} times 5 mathrm{cm} times ) ( 7 mathrm{cm} ) are to be painted. If there are 60 bricks, find the total area to b painted. | 9 |

386 | The Total Surface Area of a cube in ( c m^{2} ) is equal to the volume of the cube in ( c m^{3} ) The edge of the cube is ( _{–}– ) (in ( mathrm{cm} ) ( A cdot 3 ) B. 4 ( c cdot 5 ) D. 6 | 9 |

387 | Find the amount of water displaced by a solid spherical ball of diameter ( 28 mathrm{cm} ) A ( cdot_{11498} frac{2}{3} c m^{3} ) В ( cdot_{11498} frac{2}{7} c m^{3} ) c. ( _{11498} frac{1}{3} c m^{3} ) D. ( _{11498} frac{2}{5} )cm( ^{3} ) | 9 |

388 | The length, breadth and height of a cuboid are in the ratio ( 5: 4: 2 . ) If the total surface area is ( 1216 mathrm{cm}^{2} ), find the dimensions of the solid. A . ( (21 times 11 times 8) mathrm{cm} ) B. ( (20 times 16 times 8) mathrm{cm} ) c. ( (27 times 17 times 8) mathrm{cm} ) D. ( (25 times 19 times 8) mathrm{cm} ) | 9 |

389 | A rectangular solid has a square base, with each side of the base measuring 4 meters. If the volume of the solid is 112 cubic meters, what is the surface area of the solid? A. ( $ 1,500 ) B. ( $ 1,700 ) ( c . $ 2,200 ) D. ( $ 3,000 ) | 9 |

390 | Three cubes whose edges measure ( 3 c m, 4 c m ) and ( 5 c m ) respectively are used to form a single cube. Find its edge. Also, find the surface area of the new cube. | 9 |

391 | The diameter of a spherical ball is 21 ( mathrm{cm} . ) How much leather is required to prepare 5 such balls. | 9 |

392 | The circumference of the base of a circular cylinder is ( 6 pi mathrm{cm} . ) The height of the cylinder is equal to the diameter of the base. How many litres of water can it hold? A . ( 0.54 pi ) litres B. ( 0.6 pi ) litres c. ( 0.5 pi ) litres D. ( 0.4 pi ) litres | 9 |

393 | If radius of sphere is doubled, what is the ratio of volume of original sphere to that of second? A . 1: 4 B . 8: 1 ( mathrm{c} cdot 1: 8 ) D. None | 9 |

394 | A road roller takes 750 complete revolutions to move once over to level a road. Find the area of road if the diameter of a road roller is ( 84 mathrm{cm} ) and length is ( 1 mathrm{m} ) | 9 |

395 | The volume of a sphere of diameter ( 2 p ) cm is given by A ( cdot pi p^{2} c m^{3} ) В ( cdot pi p^{3} c m^{3} ) ( mathbf{c} cdot 4 pi p^{3} c m^{3} ) D. ( frac{4}{3} pi p^{3} c m^{3} ) | 9 |

396 | The ( T S A ) of cube ( =726 mathrm{cm}^{2} ) find the edge. | 9 |

397 | The percentage increase in the surface area of a cube when each side is increased to ( frac{3}{2} ) times the original length is A . 225 в. 200 c. 175 D. 125 | 9 |

398 | Find the volume of a sphere whose surface area is ( 154 mathrm{cm}^{2} ) | 9 |

399 | A copper rod of radius ( 1 mathrm{cm} ) and length 2 ( mathrm{cm} ) is drawn into a wire of length ( 18 mathrm{m} ) of uniform thickness. Find the thickness of the wire. | 9 |

400 | From a solid wooden cube of sides ( 14 mathrm{cm} ) a biggest hemispherical depression is carved out. What is the total surface area of the remain solid? | 9 |

401 | Volume and surface area of a solid hemisphere are numerically equal then what is the diameter of hemisphere? | 9 |

402 | A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 ( mathrm{m} ) by ( 14 mathrm{m} . ) Find the height of the platform. | 10 |

403 | If the diagonal of cube is ( sqrt{300} mathrm{cms} ) then the surface area (in sq. cm) is A. 300 B. 600 ( c cdot 1200 ) D. 2400 | 9 |

404 | The diameters of the internal and external surfaces of a hollow spherical shell are ( 6 mathrm{cm} ) and ( 10 mathrm{cm} ) respectively. If it is melted and recast into a solid cylinder of diameter ( 14 c m, ) find the height of the cylinder. | 9 |

405 | If ( s ) represents the side, then the formula of surface area of cube is A ( cdot 6(s)^{2} ) 2) ( ^{6}left(a^{prime}right)^{6} ) B. ( 3(s)^{2} ) ( c cdot 5(s)^{2} ) D・ ( 16(s)^{2} ) | 9 |

406 | Show that the height of a closed right circular cylinder of given volume and least surface area is equal to its diameter. | 9 |

407 | A hemisphere bowl is made of steel of ( 0.25 mathrm{cm} ) thickness. The inner radius of the bowl is ( 5 mathrm{cm} . ) The volume of steel used is ( _{-}-_{-}-_{-}-_{-}-_{-} cdot(pi=mathbf{3 . 1 4 1}) ) ( mathbf{A} cdot 42.15 mathrm{cm}^{3} ) B . ( 41.52 mathrm{cm}^{3} ) c. ( 41.24 mathrm{cm}^{3} ) D. ( 40 mathrm{cm}^{3} ) | 9 |

408 | A solid cuboid of iron with dimensions ( 53 c m times 40 c m times 15 c m ) is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are ( 8 mathrm{cm} ) and ( 7 mathrm{cm} ) respectively. Find the length of pipe. | 10 |

409 | Water is being pumped out through a circular pipe whose internal diameter ( 7 mathrm{cm} . ) If the flow of water is ( 72 mathrm{cm} ) per second, how many liters of water are being pumped out in one hour? | 9 |

410 | If the radius of a sphere is increased by ( 2 mathrm{cm}, ) then its surface area increases by ( 352 c m^{2} . ) The radius of the sphere before the increase was A. ( 3 mathrm{cm} ) B. ( 4 mathrm{cm} ) ( c .5 mathrm{cm} ) D. ( 6 mathrm{cm} ) | 9 |

411 | If the surface area of a sphere is ( 144 pi mathrm{cm}^{2}, ) then its radius is: ( A cdot 6 c m ) B. ( 8 mathrm{cm} ) ( mathrm{c} cdot 12 mathrm{cm} ) D. ( 10 mathrm{cm} ) | 9 |

412 | The hollow sphere, in which the circus motor cylist performs his stunts, has a diameter of ( 7 mathrm{m} ). Find the area available to the motor cylist for riding. | 9 |

413 | The ratio of the volumes of two spheres is ( 8: 27 . ) The ratio of their radii is A .3: 2 B. 2: 3 c. 4: 3 D. 2: 9 | 9 |

414 | Each edge of a cube is increased by ( 50 % ) The percentage increase in the surface area of the cube is A . 50 в. 125 ( c .150 ) D. 225 | 9 |

415 | Water flows out through a circular pipe whose internal diameter is ( 2 mathrm{cm} ), at the rate of 6 metre per second into a cylindrical tank, the radius of whose base is ( 60 mathrm{cm} ). By how much will the level of water rise in 30 minutes? A ( .2 m ) в. ( 3 m ) ( c .4 m ) D. ( 5 m ) | 9 |

416 | A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is ( 84 mathrm{cm} ) and length is ( 1 mathrm{m} ) | 9 |

417 | The volume of a sphere of radius ( r ) is: A ( cdot frac{4}{3} pi r^{3} ) В. ( 2 pi r^{2} ) c. ( frac{2}{3} pi r^{3} ) D. ( 4 pi r^{2} ) | 9 |

418 | A metallic cylinder of diameter ( 5 mathrm{cm} ) and height ( 3 frac{1}{3} mathrm{cm} ). is melted cast into a sphere. What is its diameter. | 9 |

419 | An open rectangular cistern when measured from outside is 1.35 m long ( 1.08 m ) broad and ( 90 mathrm{cm} ) deep. It is made up of iron, which is ( 2.5 mathrm{cm} ) thick. Find the capacity of the cistern and the volume of the iron used. | 10 |

420 | en The capacities of two hemispher- ical vessels are 6.4 litres and 21.6 litres. The ratio of their in- ner radii is (1) 4:9 (2) 16: 81 (3) 2 : 13 (4) 2:3 | 9 |

421 | The volume of a sphere is ( 300.5 mathrm{cm}^{3} ) Find its surface area. A . ( 21.3146 mathrm{cm} ) в. ( 216.3146 mathrm{cm}^{2} ) ( mathbf{c} cdot 216.3146 mathrm{mm}^{2} ) D. ( 216.3146 mathrm{m}^{2} ) | 9 |

422 | The curved surface area of a hemisphere of diameter 2 r is ( begin{array}{l}text { A } 2 pi r^{2} \ ^{2}+2 r r^{2} \ ^{2}end{array}^{2} ) В. ( 3 pi r^{2} ) ( mathbf{c} cdot 4 pi r^{2} ) D. ( 8 pi r^{2} ) | 9 |

423 | The radius of a sphere is ( 10 mathrm{cm} ). If the radius is increased by ( 1 mathrm{cm} ), then prove that volume fo the sphere is increased by ( 33.1 % ) | 9 |

424 | Three equal cubes are placed in a row touching each other Find the ratio of the total surface area of the resulting cuboid to that of the sum of surface areas of the three cubes A . 5: 7 B. 7:9 c. 9: 7 D. None of these | 9 |

425 | The volume of the global hemisphere is ( 19404 i n^{3} . ) Find its diameter. A . 21 in B. 42 in c. 10.5 in D. 9 in | 9 |

426 | 55. A cylinder has ‘r’ as the radius of the base and ‘h’ as the height. The radius of base of another cylinder, having double the vol- ume but the same height as that of the first cylinder must be equal (2) 27 (1) 5 (3) r2 (4) der | 10 |

427 | A small village, having a population of ( 5000, ) requires 75 litres of water per head per day. The village has got an overhead tank of measurement ( 40 mathrm{m} ) ( times 25 mathrm{m} times 15 mathrm{m} . ) For how many days will the water of this tank last? | 10 |

428 | If the total surface area of a solid hemisphere is ( 462 mathrm{cm}^{2} ), find its volume. ( left[text { take } boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) | 9 |

429 | The largest sphere is carved out of a cube whose edge is of length ( l ) units. Find the volume of the sphere. A ( cdot frac{5 pi l^{3}}{6} ) в. ( frac{3 pi l^{3}}{5} ) с. ( frac{pi l^{3}}{6} ) D. ( frac{2 pi l^{3}}{7} ) | 9 |

430 | What will happen to the volume of the cube, if its edge is (a) tripled (b) reduced to one-fourth? | 9 |

431 | A cube has ( _{text {the }} ) egdes vertices | 9 |

432 | The curved surface area and height of a cylinder are ( 110 mathrm{cm}^{2} ) and ( 5 mathrm{cm} ) respectively. Find the radius of a cylinder. | 9 |

433 | Two cubes each with ( 12 mathrm{cm} ) are joined end to end. Find the surface area of the resulting cuboid. | 9 |

434 | Find the later surface area and total surface area of the following right prisms. | 9 |

435 | A rectangle of sides ( 5 mathrm{cm} ) and ( 7 mathrm{cm} ) are rotated along the side ( 7 mathrm{cm} ) Find the volume of solid so obtained. | 9 |

436 | A cylinder of height ( 90 mathrm{cm} ) and base diameter ( 8 c m ) is melted and recast into spheres of diameter ( 12 mathrm{cm} ). Find the number of spheres. | 10 |

437 | If each edge of cuboid of surface area ( boldsymbol{S} ) is doubled, then surface area of the new cuboid is A . ( 2 S ) B. ( 4 S ) ( c cdot 6 S ) D. ( 8 S ) | 9 |

438 | The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius ( 3 mathrm{cm} ) and height 7 ( mathrm{cm} ) is ( mathbf{A} cdot 108 pi c m^{3} ) в. ( 36 pi c m^{3} ) c. ( 12 pi c m^{3} ) D. ( frac{4}{3} pi c m^{3} ) | 9 |

439 | The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of 10 per ( m^{2} ) is 15000, find the height of the hall (in meters). | 9 |

440 | A cylindrical cistern whose diameter is ( 21 c m ) is partly filled with water. If a rectangular block of iron ( 14 mathrm{cm} ) in length, ( 11 c m ) in breadth and ( 12 c m ) in thickness if wholly immersed in water, by how many centimetres will the water level rise? ( left(boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right) ) | 9 |

441 | A rectangular room is ( 6 m ) long, ( 5 m ) wide and ( 4 m ) high. Find the total surface area of the four walls. | 9 |

442 | Cylinder ( A ) has diameter ( 14 mathrm{cm}, ) and the height is ( 7 mathrm{cm}, ) and cylinder ( B ) has diameter ( 7 mathrm{cm} ) and height is ( 14 mathrm{cm} ) Without calculation tell volume of which cylinder is more? Verify the answer by calculation | 9 |

443 | A hemispherical bowl of internal radius ( 15 c m ) contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter ( 5 mathrm{cm} ) and height ( 6 mathrm{cm} . ) How many bottles are necessary to empty the bowl? | 10 |

444 | Find the ( T . S . D ) of a cube, whose volume is ( 3 sqrt{3} a^{3} ) cubic units. | 9 |

445 | A dome of a building is in the form of a hemisphere. From inside, it ws white- washed at the cost of RS. ( 498.96 . ) If the ( operatorname{cost} ) of white-washing is Rs. 2.00 per square metre, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome. | 9 |

446 | Curved surface area of solid sphere is ( 24 c m^{2} . ) If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is : ( mathbf{A} cdot 12 c m^{2} ) в. ( 8 c m^{2} ) ( mathbf{c} cdot 16 mathrm{cm}^{2} ) D. ( 18 mathrm{cm}^{2} ) | 9 |

447 | If the volume of a solid sphere is ( 7241 frac{1}{4} c u . c m, ) then find its radius. ( left(text { Take } pi=frac{22}{7}right) ) | 9 |

448 | The rain water that falls on a roof of area ( 6160 m^{2} ) is collected in a cylindrical tank of diameter ( 14 mathrm{m} ) and height ( 10 mathrm{m} ) and thus the tank is completely filled. Find the height of rain water on the roof. | 9 |

449 | The height of a cuboid is ( 18 mathrm{m} ). Its length is 3 times its height and 2 times its width. Find the surface area of the cuboid. ( mathbf{A} cdot 5280 m^{2} ) В. ( 5832 m^{2} ) c. ( 5313 m^{2} ) D. ( 5188 m^{2} ) | 9 |

450 | Two spheres have their surface areas in the ratio ( 4: 9 . ) Their volumes are in the ratio ( boldsymbol{m}: boldsymbol{n} . ) Find ( boldsymbol{m}+boldsymbol{n} ) | 9 |

451 | A door of length ( 2 m ) and breadth 1 m is fitted in a wall. The length of the wall is 4.5 and the breadth is 3.6 m. Find the ( operatorname{cost} ) of the wall washing the wall, if the rate white washing the wall is ( R s .20 ) per ( boldsymbol{m}^{2} ) | 9 |

452 | Find the volume of a sphere whose surface area is ( 55.44 mathrm{cm}^{2} . ) (Take ( pi=frac{22}{7} ) ( mathbf{A} cdot 38.808 mathrm{cm}^{3} ) B. ( 38.008 mathrm{cm}^{3} ) c. ( 32.808 mathrm{cm}^{3} ) D. ( 28.808 mathrm{cm}^{3} ) | 9 |

453 | A sphere has volume ( 36 pi c m^{3} ), find the radius of the sphere A ( .4 mathrm{cm} ) B. 3 cm ( c .6 c m ) D. 8 ст | 9 |

454 | How many cubic metres of earth must be dug to make a well 14 metres deep and 4 metres in diameter? | 9 |

455 | Find the volume of cylinder, if the radius of its base is ( 1.5 mathrm{cm} ) and its height is ( mathbf{5} c m ) | 9 |

456 | A spherical glass vessel has a cylindrical neck which is ( 4 mathrm{cm} ) long and ( 2 mathrm{cm} ) in diameter. The diameter of the spherical part is ( 6 mathrm{cm} ). Find the amount of water it can hold? | 9 |

457 | A hollow spherical shell is made of metal of density ( 4.8 mathrm{g} / mathrm{cm}^{3} . ) If its internal and external radii are ( 10 mathrm{cm} ) and ( 12 mathrm{cm} ) respectively, find the weight of the shell A. ( 15.24 mathrm{kg} ) B . ( 12.84 mathrm{kg} ) c. ( 14.64 mathrm{kg} ) D. None of these | 9 |

458 | The volume of a cube is numerically equal to the sum of its edges. What is the total surface area in square units? ( mathbf{A} cdot 66 ) в. 183 ( c .36 ) D. 72 | 9 |

459 | Find the surface area of a sphere of diameter: ( mathbf{3 . 5} mathrm{cm} ) | 9 |

460 | It cost Rs 4020 to paint the inner curved surface area of hemisphere of radius 8 ( m ). If it is painted at rate of Rs. 10 per ( m^{2} ). Find inner curved surface. A. ( 402 m^{2} ) в. ( 400 mathrm{m}^{2} ) c. ( 200 m^{2} ) D. ( 201 m^{2} ) | 9 |

461 | The vol of a cube ( =1000 mathrm{cm}^{3} ), Find its TSA in ( c m^{2} ) | 9 |

462 | The capacity of a closed cylindrical vessel of height ( 1 mathrm{m} ) is 15.4 litres. How many square meters of metal sheet would be needed to make it? | 9 |

463 | A copper rod of diameter ( 1 mathrm{cm} ) and length ( 8 mathrm{cm} ) is drawn into a wire of length ( 18 mathrm{cm} ) of uniform thickness. Find the thickness of the wire. | 9 |

464 | Find the surface area of a sphere (in ( c m^{2} ) ) of radius: ( 14 mathrm{cm} ) | 9 |

465 | 2 cubes of volumes ( 664 mathrm{cm}^{3} ) are joined end to end. Fin the surface area of the reacting cuboid. | 9 |

466 | The crossection of a canal is a trapezium. The breadths of the top and bottom of the canal are ( 8 m ) and ( 6 m ) respectively. If the earth of volume ( 112 times 10^{4} m^{3} ) is taken out to build the canal of ( 50 mathrm{km} ) long, then the depth of the canal will be ( mathbf{A} cdot 3.2 m ) B. ( 3.8 m ) c. ( 4.0 m ) D. 4.2 ( m ) | 9 |

467 | The energy required to blow a bubble of radius ( 4 mathrm{cm} ) and ( 3 mathrm{cm} ) in the same liquid is in the ratio of A .4: 3 B. 3:4 ( c cdot 16: 9 ) D. 64 : 27 | 9 |

468 | A large solid sphere of diameter ( 18 mathrm{cm} ) is melted and recast into several small spheres of diameter ( 3 mathrm{cm} ) The percentage increase in the surface area of the smaller spheres over that of the larger sphere is A . 500% B . 350% c. ( 450 % ) D. 545% | 9 |

469 | A solid has hemispherical base with diameter ( 8.5 mathrm{cm} ) and it is surmounted by a cylinder height ( 8 mathrm{cm} ) and diameter of cylinder is ( 2 mathrm{cm} ). Find the volume of this solid. ( (pi=3.14) ) | 9 |

470 | The length of an edge of a cube is ( l ). Find the formula for the sum of lengths of all the edges of the cube | 9 |

471 | The diameter of a right circular cylinder is decreased by 10%. The volume of cylinder remains the same then the percentage increase in height is: A . 20% B. 23.45% c. 5% D. 20.5% | 9 |

472 | The radius of a spherical balloon increases from ( 7 mathrm{cm} ) to ( 14 mathrm{cm} ) as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases. A .1: 4 B . 4: 1 c. 1: 2 D. 2: 1 | 9 |

473 | A lead ball of radius ( 24 mathrm{cm} ) is melted down and recast into smaller balls of radius ( 6 mathrm{cm} . ) Assuming that no metal is lost in this process, number of complete smaller balls that can be made, is – A . 4 B . 16 ( c .36 ) D. 64 | 9 |

474 | The hollow sphere, in which the circus motorcyclist performs his stunts, has diameter of 7 m. Find the area available to motorcyclist for riding. A ( .154 mathrm{m}^{2} ) B. ( 144 mathrm{m}^{2} ) c. ( 38.5 mathrm{m}^{2} ) D. ( 176 m^{2} ) | 9 |

475 | Assertion If a ball in the shape of a sphere has a surface area of ( 221.76 mathrm{cm}^{2}, ) then its diameter is ( 8.4 mathrm{cm} ) Reason If the radius of the sphere be ( r, ) then surface area, ( S=4 pi r^{2}, ) i.e. ( r=frac{1}{2} sqrt{frac{s}{pi}} ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 9 |

476 | Find the volume of a sphere of radius ( 2.1 mathrm{cm}left(text { use } pi=frac{22}{7}right) ) | 9 |

477 | The volume of sphere with radius ( 3 c m ) is ( c m^{3} ) A . ( 14 pi ) B. ( 18 pi ) ( c cdot 2 pi ) D. ( 36 pi ) | 9 |

478 | If the surface area of a sphere is ( 9856 c m^{2} . ) Find its diameter. A . 28 B. 55 ( c .56 ) D. 30 | 9 |

479 | Total surface area of a cube is ( 54 mathrm{cm}^{2} ) Then its side is ( mathbf{A} cdot mathbf{6} ) B. 9 c. 12 D. 3 | 9 |

480 | A sphere and the base of a cylinder have equal radii. The diameter of the sphere is equal to the height of the cylinder. The ratio of the curved surface area of the cylinder and surface area of the sphere is A . 1: 1 B. 2: 3 c. 3: 2 D. 1: 2 | 9 |

481 | The radius of base of a right circular cylinder is halved and its height is increased by ( 50 % ). The ratio of volume of the new cylinder to that of the original cylinder will be A . 3: 8 B. 2: ( c cdot 3: 1 ) ( D cdot 4: ) | 9 |

482 | In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter ( 5 mathrm{cm} . ) Find the total radiating surface in the system. A ( cdot 4.4 m^{2} ) B . ( 2.4 m^{2} ) c. ( 4.1 mathrm{m}^{2} ) D. ( 3.4 m^{2} ) | 9 |

483 | Find the volume of the recycled material used in making the solid as shown in figure. It is given that diameter of cylinder is ( 20 mathrm{cm} ) and diameter of each of two equal conical cavity is ( 10 mathrm{cm} ) What values are reflected by using recycled material? | 9 |

484 | Ps. 3. A tent is made in the form of a cone surmounted by another diameter of the ends of the fru height is 3 m and the height of the area of the canvas required. ade in the form of a frustrum A of a right circular ounted by another right circular cone B. The I the ends of the frustrum A are 8 m and 4 m, its ? and the height of the cone B is 2 m. Find the (1979) In col.1 | 10 |

485 | Curved surface area and circumference at the base of a solid right circular cylinder are 4400 sq. ( mathrm{cm} ) and ( 110 mathrm{cm} ) respectively. Find its height and diameter. | 9 |

486 | Find the cost of white washing the four walls of a cubical room of side ( 4 m ) at the rate of ( boldsymbol{R} boldsymbol{s} . boldsymbol{2} boldsymbol{0} / boldsymbol{m}^{2} ) | 9 |

487 | The diameter of a sphere is decreased by ( 25 % . ) By what percent does its curved surface area decrease? A . ( 53.85 % ) B. ( 34.85 % ) c. ( 45.65 % ) D. ( 43.75 % ) | 9 |

488 | The radius of a sphere is ( 2 r, ) then find its volume | 9 |

489 | From a solid cylinder whose height is ( 2.4 mathrm{cm} ) and diameter ( 1.4 mathrm{cm}, ) a concial cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm. | 9 |

490 | 59. A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with maxi- mum height of 13.5 metres above the ground. If the radius of the base is 14 metres, the cost of painting the inner side of the tent at the rate of Rs. 2 per square metre is (1) Rs. 2,050 (2) Rs. 2,060 (3) Rs. 2,068 (4) Rs. 2,080 | 10 |

491 | If the perimeter of one face of a cube is ( 20 mathrm{cm}, ) then its surface area is A ( cdot 120 mathrm{cm}^{2} ) в. ( 150 mathrm{cm}^{2} ) ( mathrm{c} cdot 125 mathrm{cm}^{2} ) D. ( 400 mathrm{cm}^{2} ) | 9 |

492 | Water flows at the rate of ( 15 k m ) per hr through a pipe of a diameter ( 14 mathrm{cm} ) into a rectangle tank which is ( 50 m ) long and ( 44 m ) wide, Find the time in which th level of water in the tank will rise by ( 21 c m ) | 9 |

493 | A dome of a building is in the form of a hemisphere. From inside, it was white- washed at the cost of ( 498.96 . ) If the costt of white-washing is 2.00 per square metre, find (i) the inside surface area of the dome and (ii) volume of the air inside the dome. | 9 |

494 | The volume of a sphere is 38808 cu.cm. The curved surface area of the sphere ( left(operatorname{in} c m^{2}right) ) is: A .5544 в. 1386 ( c .8316 ) D. 4158 | 9 |

495 | The volume of a sphere is ( frac{4}{3} pi r^{3} c . c . ) What is the ratio of the volume of a cube to that of a sphere which will fit inside the cube? ( mathbf{A} cdot 4: 3 pi ) в. ( 2: pi ) ( c cdot 8: pi ) D. ( 6: pi ) | 9 |

496 | 15 circular plates, each of radius ( 7 mathrm{cm} ) and thickness ( 3 mathrm{cm} ) are placed one above the another to form a cylindrical solid. Find the volume of the cylinder so formed | 10 |

497 | Find the amount of water displaced by a solid spherical ball of diameter ( 0.21 mathrm{cm} ) | 9 |

498 | The largest sphere is carved out of a cube of edge ( 14 mathrm{cm} . ) Then the volume of the sphere is A ( . ) 1370 ( c m^{3} ) B . ( 1800 mathrm{cm}^{3} ) c. ( 1437 mathrm{cm}^{3} ) D. ( 1734 mathrm{cm}^{3} ) | 9 |

499 | 60. A right circular cylinder just en- closes a sphere of radius r. The ratio of the surface area of the sphere and the curved surface area of the cylinder is (1) 2:1 (2) 1:2 (3) 1:3 (4) 1:1 | 9 |

500 | The ratio between the curved surface area and the total surface area of a right circular cylinder is ( 1: 2 . ) Find the volume of the cylinder if its total surface area is ( 616 mathrm{cm} ) sq. | 9 |

501 | Find the volume of a sphere of radius 3 ( mathrm{cm} ) | 9 |

502 | The metallic cuboid ( 100 mathrm{cm} times 80 mathrm{cm} times ) ( 64 mathrm{cm} ) is recast into a cube. The surface area of the cube is A ( cdot 19200 mathrm{cm}^{2} ) B. ( 31600 mathrm{cm}^{2} ) c. ( 38400 mathrm{cm}^{2} ) D. ( 25600 mathrm{cm}^{2} ) | 9 |

503 | How many faces a cube has? A .4 B. 6 c. 8 D. 12 | 9 |

504 | Find the volume of a sphere-shaped metallic shotput having a diameter of ( 8.4 mathrm{cm}left(text { Take } pi=frac{22}{7}right) ) | 9 |

505 | The area of a side of a box is 120 sq. ( mathrm{cm} ) The area of the other side of the box is 72 sq. ( mathrm{cm} . ) If the area of the upper surface of the box is 60 sq. ( mathrm{cm} ), then find the volume of the box. ( mathbf{A} cdot 259200 mathrm{cm}^{3} ) B. ( 84000 mathrm{cm}^{3} ) c. ( 86400 c m^{3} ) D. ( 720 mathrm{cm}^{3} ) | 10 |

506 | A square hole of cross – sectional area ( 4 c m^{2} ) is drilled across a cube with its length parallel to a side of the cube. If edge of the cube measures ( 5 c m, ) what is the total surface area of the body so formed? A ( cdot 140 mathrm{cm}^{2} ) В. ( 142 mathrm{cm}^{2} ) ( mathrm{c} cdot 162 mathrm{cm}^{2} ) D. ( 182 mathrm{cm}^{2} ) | 9 |

507 | 65. If the sum of three dimensione and the total surface area of a rectangular box are 12 cm and 94 cm respectively, then the maximum length of a stick that can be placed inside the box is (1) 52 cm (2) 5 cm (3) 6 cm (4) 2 5 cm | 9 |

508 | Which of the following is a unit of Volume? A. Meters per second B. Cubic millimeters c. Litres D. Both B and C | 9 |

509 | 62. A right cylindrical vessel is full with water. How many right cones having the same diam- eter and height as that of the right cylinder will be needed to store that water ? (Take it = 22 07 (1) 4 (3) 3 (2) 2 (4) 5 | 10 |

510 | or is dug 59. A well 20 m in diameter is a 14 m deep and the earth take out is spread all around it to width of 5 m to form an embank ment. The height of the embank ment is (1) 10 m (2) 11 m (3) 11.2 m (4) 11.5 m | 10 |

511 | Each edge of a cube is increased by ( 50 % ). The per cent of increase in the surface area of the cube is A. 50 B. 125 c. 750 D. 300 | 9 |

512 | A sphere, cylinder ( & ) a cone gave the same radius ( & ) same height, find the ratio of their curved surface areas. | 9 |

513 | A rocket is in the shape of a cone mounted on a right circular cylinder their common base diameter is ( 8 mathrm{cm} ) the height of cylindrical and concial shapes are ( 6 mathrm{cm} ) and ( 3 mathrm{cm} ) respectively. Find the volume of the rocket. | 10 |

514 | State True(1) or False(O) A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is ( frac{4}{3} pi a^{3} ) | 9 |

515 | A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet? A .261 .8 B. 785.4 ( c .916 .3 ) D. 1,047.2 | 10 |

516 | Find the curved surface area of a cylinder given above: A ( cdot 1507.2 m^{2} ) в. ( 1527.6 m^{2} ) ( c cdot 1517.8 m^{2} ) D . ( 1588.1 m^{3} ) | 9 |

517 | The diameter of the base of the cylinder is ( 12 mathrm{cm} ) and the height is ( 8 mathrm{cm} . ) Find the surface area of the solid cylinder. A ( cdot 520 mathrm{cm}^{2} ) B. ( 524 mathrm{cm}^{2} ) ( mathrm{c} cdot 528 mathrm{cm}^{2} ) D. ( 532 mathrm{cm}^{2} ) | 9 |

518 | Find the total surface of cuboid whose length is ( 8 c m ) breadth is ( 6 mathrm{cm} ) and height is ( 5 c m ) | 10 |

519 | How many balls each of radius ( 1 mathrm{cm} ) can be made from a copper sphere whose radius is ( 8 mathrm{cm} ? ) | 9 |

520 | The radius of a hemispherical balloon increases from ( 7 mathrm{cm} ) to ( 14 mathrm{cm} ) as air is being pumped into it. Find the ratios of the surface areas of the balloon in the two cases. | 9 |

521 | Find the volume of a cube if its total surface area is 294 sq ( c m ) | 9 |

522 | The volume of a rectangular block of stone is ( 10368 d m^{3} ) Its dimensions re in the ratio 3: 2: 1 If its entre surface is polished at 2 paise per ( d m^{2} ) then the total cost will be ( A cdot R s 31.50 ) B. Rs 31.68 c. Rs 63 D. Rs 63.36 | 9 |

523 | Find the volume of hemisphere of radius ( 3.5 mathrm{cm} ) | 9 |

524 | A semicircular piece of paper of radius ( 14 mathrm{cm} ) is rolled to form a cone of the largest possible size. Find the capacity of the cone. A ( cdot 721.5 mathrm{cm}^{3} ) B. ( 645.10 mathrm{cm}^{3} ) c. ( 449.64 mathrm{cm}^{3} ) D. ( 622.37 mathrm{cm}^{3} ) | 10 |

525 | Find the lateral surface area and total surface area of a cuboid which is ( 8 mathrm{m} ) long, ( 5 mathrm{m} ) broad and ( 3.5 mathrm{m} ) high. | 9 |

526 | An ice-cream cone consisting of the cone is surmounted by a hemisphere.The common radius of a hemisphere ( & ) cone is ( 3.5 mathrm{cm} ) & the total height of ice cream is ( 12.5 mathrm{cm} ) Calculate the volume of ice-cream in the solid shape. | 10 |

527 | Find the ratio of the volume of sphere ( boldsymbol{A} ) to sphere ( B ), if the ratio of the surface area of sphere ( A ) to the surface area of sphere ( boldsymbol{B} ) is ( mathbf{7 2 9}: mathbf{1} ) A .27: 1 в. 81: 1 C. 19,683: 1 D. 26,224: 1 E . 531,441: 1 | 9 |

528 | The length of the side is ( 3.9 mathrm{ft} ). Find the surface area of a cube . A ( cdot 41.82 f t^{2} ) B. ( 94.16 f t^{2} ) c. ( 91.26 f t^{2} ) D. ( 40.41 f t^{2} ) | 9 |

529 | It is required to fix a pipe such that water flowing through it at a speed of ( 7 m ) per minutes fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be: A. ( sqrt{2} m ) в. ( 2 m ) c. ( frac{1}{2} m ) D. ( frac{1}{sqrt{2}} m ) | 9 |

530 | A rectangular pipe of metal ( 16 mathrm{cm} times 32 ) ( mathrm{cm} ) rolled along its length and a cylinder is formed. Find the surface area of the cylinder. (Use ( left.boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right) ) A ( .532 .13 mathrm{cm}^{2} ) B. ( 542.13 mathrm{cm}^{2} ) c. ( 552.13 c m^{2} ) D. ( 562.13 mathrm{cm}^{2} ) | 10 |

531 | A cubical water tank measures 3 feet sides. Find its surface area. A ( .9 f t^{2} ) B. ( 50 f t^{2} ) c. ( 52 f t^{2} ) D. ( 54 f t^{2} ) | 9 |

532 | Find the volume of a sphere ( left(operatorname{in} m^{3}right) ) whose diameter is : 2.1 ( mathrm{m} ) | 9 |

533 | 59. The radius of the base of a right circular cone is doubled. To keep the volume fixed, the height of the cone will be (1) one-fourth of the previous height (2) 5 times of the previous height (3) half of the previous height (4) one-third of the previous height | 10 |

534 | The length of the shortest face diagonal of a cuboid of dimensions ( 5 mathrm{cm} times 4 mathrm{cm} times ) ( 3 mathrm{cm} ) is ( _{–}-_{-}(text {in } mathrm{cm}) ) ( A cdot 4 ) B. 5 ( c cdot 6 ) D. | 9 |

535 | A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is ( 10 mathrm{cm} ) when flat circular surface is downward. Find the level of the water, when it is inverted upside down, common diameter is ( 7 mathrm{cm} ) and height of the cylinder is ( 20 mathrm{cm} ) | 9 |

536 | The volume of a cube is ( 1000 mathrm{cm}^{3} ). Find its total surface area in ( mathrm{cm}^{2} ) | 9 |

537 | The cube has volume 64 cubic units. If a largest sphere possible that can be placed inside this cube has radius ( r ) then the value of ( r ) is A . 2 B. ( 2 sqrt{2} ) ( c cdot 4 ) D. 8 | 9 |

538 | The area of the curved surface of a sphere is ( 5544 m^{2} ). Find the radius of the sphere A. 12 m в. ( 20 mathrm{m} ) ( c .22 mathrm{m} ) D. ( 21 mathrm{m} ) | 9 |

539 | A cylinder vessal open at the top has diameter ( 20 mathrm{cm} ) and height ( 14 mathrm{cm} . ) Find the cost of tin-plating it on the inside at the rate of 50 paisa per hundred square centimeter. | 9 |

540 | Volume and total surface area of a solid hemisphere are equal in magnitude. The volume is expressed in ( mathrm{cm}^{3} ) and the area is expressed in ( mathrm{cm}^{2} ). Find the radius of hemisphere. A. ( 3 mathrm{cm} ) B. ( 4 mathrm{cm} ) c. ( 4.5 mathrm{cm} ) D. ( 5.5 mathrm{cm} ) | 9 |

541 | A cylindrical container of radius ( 6 mathrm{cm} ) and height ( 15 mathrm{cm} ) is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone. | 10 |

542 | Figure shows a semicircle that is the graph of the equation ( y=sqrt{6 x-x^{2}} ). the semicircle is rotated ( 360^{circ} ) about the ( x ) -axis, calculate the volume of the sphere that is created ( A cdot 6 pi ) В. ( 12 pi ) ( c .18 pi ) D. ( 24 pi ) E. ( 36 pi ) | 9 |

543 | Consider a cuboid all of whose edges are integers and whose base is a square. Suppose the stun of all its edges is numerically equal to the sum of the areas of all its six faces. Then the sum of all its edges is A ( cdot 12 ) B. 18 ( c cdot 24 ) D. 36 | 9 |

544 | A hemispherical bowl is made of steel ( 0.25 c m ) thick. The inside radius of the bowl is ( 5 mathrm{cm} ). Find the volume of steel used in making the bowl in ( c m^{3} ) | 9 |

545 | A rectangular tank ( 28 m ) long and ( 22 m ) wide is required to receive entire water from a full cylindrical tank of internal diameter ( 28 m ) and depth ( 4 m . ) Find the least height of the tank that will serve the purpose. (Take ( boldsymbol{pi}=mathbf{2 2} / mathbf{7}) ) A. ( 4.0 mathrm{m} ) в. ( 4.5 mathrm{m} ) ( c .5 .0 m ) D. ( 5.2 m ) | 10 |

546 | A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is ( 30 mathrm{cm} ) long, ( 25 mathrm{cm} ) wide and ( 25 mathrm{cm} ) high. (i) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges? | 9 |

547 | The radius of a sphere is ( 2 r, ) then its volume will be: A ( cdot frac{4}{3} pi r^{3} ) В. ( 4 pi r^{3} ) c. ( frac{8 pi r^{3}}{3} ) D. ( frac{32}{3} pi r^{3} ) | 9 |

548 | The surface area of a cube is ( 441 m^{2} ) Find its side. ( mathbf{A} cdot 8.5 mathrm{m} ) B. ( 8.2 mathrm{m} ) c. ( 8.1 mathrm{m} ) D. ( 8.4 mathrm{m} ) | 9 |

549 | Find the surface area of a ( 10 mathrm{cm} times ) ( 4 c m times 3 c m ) brick: A. 84 sq. ( mathrm{cm} ) B. 124 sq.cm c. 164 sq.cm D. 180 sq.cm | 9 |

550 | The dimensions of a cuboid tin are ( 30 mathrm{cm} times 40 mathrm{cm} times 50 mathrm{cm} . ) Find the cost of tin required for making 20 such tins, If the cost of tin sheet is ( R s .20 ) per ( s q . m ) | 9 |

551 | Two cubes, each of side ( 4 mathrm{cm} ) are joined end to end. Find the surface area of the resulting cuboid | 9 |

552 | 61. A hollow iron pipe is 21 cm lo and its exterior diameter is 8 cm If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3 then the weight of the pipe is (Take n = 22 (1) 3.696 kg (2) 3.6 kg (3) 36 kg (4) 36.9 kg | 10 |

553 | Find the surface area of a cone ( mathbf{A} cdot 8635 m^{2} ) ( mathbf{B} cdot 86.35 m^{2} ) c. ( 0.8635 m ) ( mathbf{D} cdot 8.635 m^{2} ) | 9 |

554 | The ( L S A ) (lateral surface area) of a cube of side ( 1 mathrm{cm} ) is ( mathbf{A} cdot 16 mathrm{cm}^{2} ) B. ( 4 mathrm{cm}^{2} ) ( mathbf{c} cdot 2 c m^{2} ) D. ( 1 mathrm{cm}^{2} ) | 9 |

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