# Surface Areas And Volumes Questions

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 NoQuestionsClass
1If 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
2Find 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
3A 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
4Find 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
5Write the number of surfaces of a right circular cylinder.9
6A 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
7Find the volume of the sphere whose
surface area is ( 9856 mathrm{cm}^{2} )
9
8A hemispherical bowl has a radius 3.5
cm. Its volume ( mathrm{cm}^{3} )
9
9How 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
10Find the total surface area of the cuboid
with ( l=4 m, b=3 m ) and ( h=1.5 m )
9
11A solid sphere and a solid hemisphere have the same total surface area. Find
the ratio of their volumes.
9
12A 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
13A 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
14If 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
15A 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
16Find the surface area of a sphere of
( mathbf{1 4} c boldsymbol{m} )
9
17State 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
18A 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
19Find the total surface area of cubes
having the following sides.
( mathbf{5} c boldsymbol{m} )
9
20The diameter of a solid hemisphere is ( 42 mathrm{cm} . ) Find its volume, curved surface
area and total surface area.
9
21The 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
22A 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
23Assume ( pi=frac{22}{7}, ) unless stated
otherwise.
Find the volume of a sphere whose
(i) ( 7 mathrm{cm} )
(ii) ( 0.63 mathrm{m} )
9
24The 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
25If 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
26The 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
27A 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
28The 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
29A 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
30Three 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
3151. 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
3258. 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
33Find 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
34The diameter of the moon is
approximately one fourth of the diameter of the earth. Find the ratio of
their surface areas.
9
35A 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
36If the volume of a sphere is numerically equal to the surface area of the sphere, then find its radius.9
37Find 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
38A 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
39Assertion
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
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
40Two 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
41The 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
42The 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
43Find 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
9
44Four 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
45A 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
46If 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
47Base surface area of a cylinder is 20
( c m^{2} ) and its height is ( 10 mathrm{cm} . ) Find the
volume of the cylinder.
9
48A 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
49The, 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
50A 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
51Find the CSA and TSA of a solid
hemisphere of radius ( 14 mathrm{cm} )
9
52A 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
53back. 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
5457. 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
55Find the radius of a sphere whose circumference and solid content have
the same numerical value.
9
56The volume of a sphere is ( 38808 mathrm{cm}^{3} )
Find its radius and surface area.
9
57The height of cylinder is ( 4 mathrm{cm} ) The
Radius of cylinder is ( 5 mathrm{cm} ) find its
volume
9
58A 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
5966.
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
60If 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
6154. 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
62A 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
63the radius of a solid hemisphere is ( 2 r )
Find its surface area.
9
64Find the total surface area of cubes
having the following sides.
( mathbf{5 . 5} boldsymbol{m} )
9
65The number of corners in a cylinder is
( A cdot 1 )
B. 2
( c .3 )
D. None
9
66Metal 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
6771.
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
68In 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
69If a largest sphere is inscribed in a cube of side ( 7 mathrm{cm} ) then find the volume of the
sphere
9
70Volume 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
71In 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
72Find the total surface area of the
following cylinders
9
73A closed box made of steel of uniform
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
74Three 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
75A 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
76What 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
77An 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
78Calculate 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
79Each face of a cube has perimeter equal
to ( 32 mathrm{cm} ). Find its surface area
9
80The 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
81The 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
82Using 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
9
83The 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
84Two 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
85The 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
86If 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
87Find 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
88Volume 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
89Four 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
90If the radius of a sphere is doubled, then its volume is increase by
( mathbf{A} cdot 100 % )
B. 200%
( c .700 % )
D. ( 800 % )
9
91A 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
92Fill in the blanks:
A point where three surface of a solid
meet is called a
9
93The 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
94Find the lateral surface area and total
surface area of the following right
prisms.
9
95If the total surface area of a solid
hemisphere is ( 46 c m^{2}, ) find its volume
10
96A 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
97Circumference of the edge of
hemispherical bowl is ( 132 mathrm{cm} ). Find the capacity of the bowl
9
98A 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
99Small 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
100An 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
101Find 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
102The 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
103Three 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
104The radius of a sphere is ( 2.1 mathrm{cm} ). Find its
surface area.
9
105A 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
106Find the volume of a right circular cylinder if the radius of its base is ( 7 mathrm{cm} )
and height is ( 15 mathrm{cm} )
9
107The diameter of a sphere is decreased by ( 25 % ). By what percent its curved
surface area decrease?
9
10866. 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
109The 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
110Sushant 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
111The 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
112A 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
113Calculate 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
114The total surface area of a cube is
( 486 mathrm{cm}^{2} . ) Calculate its edge
9
115Find 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
116A 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
117The ( L=12 mathrm{cm}, b=10 mathrm{cm}, h=8 mathrm{cm} )
of a room. Find the total area of 4 walls.
9
118A 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
119The 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
120The 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
121A 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
122Find a cylinder which would have the
greatest volume for the given area ( S ) of
its total surface.
9
123The 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
124If 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
125The 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
126A 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
127Three 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
128Find approximately the volume of the
9
129A right circular cylinder has Height as
( 30 c m ) and Radius as ( 35 c m ) find its
( boldsymbol{C S A} )
9
130The 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
131The 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
132A 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
133Find the total surface area of a solid
hemisphere of radius ( 10 mathrm{cm} . ) [Use ( pi= )
3.14]
9
134If total surface area of a cube is
( 150 mathrm{cm}^{2}, ) find the edge.
9
135Two cubes of edge ( 6 mathrm{cm} ) are joined to
form a cuboid. Find the total surface
area of the cuboid.
9
136Assume 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
137The 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
138The 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
13958. 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
140Find the total surface area of cubes
having the following sides.
( mathbf{3} c boldsymbol{m} )
9
141If 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
142A 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
143The 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
144Length of side of cube is ( 2 a ), then the
length of diagonal is
10
145Find the surface area of the hemisphere
whose radius is ( 7 mathrm{cm} )
9
146A 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
147Suhail 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
148Find 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
14959. 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
height of the cone is :
(1) 54 cm (2) 27 cm
(3) 18 cm (4) 9 cm
10
150A 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
151How 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
152The 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
153The 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
154Praveen 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
155If 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
156An 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
15752. 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
158Find the surface area of a sphere of
radius: ( 10.5 mathrm{cm}left(text { in } c m^{2}right) )
9
159A 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
160By 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
161The 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
162What is the ratio of volumes of spheres and hemisphere?
A .2: 1
B. 4: 3
c. 2: 3
D. 1: 2
9
163A 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
164The 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
165Seven 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
166A 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
167How 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
168The 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
169A 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
170A 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
171Determine the ratio of the volume of a
cube to that of a sphere which will exactly fit inside the cube.
9
172Three 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
173A 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
174A 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
175The 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
176Find 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
177A 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
178The 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
179A solid having six equal square faces is called a
A. Cube
B. Cuboid
c. Square
D. Rectangle
9
180If 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
181Find the radius of a sphere whose
surface area is ( 154 mathrm{cm}^{2} )
9
182Which 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
183A hemispherical bowl has inner
diameter ( 11.2 mathrm{cm} . ) Find the volume of
milk it can hold.
9
184A 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
18551. 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
186A 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
187The 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
188The 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
189Find the surface area of a sphere of radius ( 1.4 mathrm{cm} .left(pi=frac{22}{7}right) )9
19055. 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
191A 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
192A 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
193The 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
194The 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
195Three 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
196A 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
197A 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
198Find the volume of a hemisphere whose radius is ( frac{mathbf{3}}{mathbf{2}} boldsymbol{c m} )9
199A 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
200A 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
201A 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
202A 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
203The 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
204A 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
205A 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
colour on its surface?
A. 20
B. 8
( c cdot 24 )
D. 32

10
206The 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
207The 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
208Find a side of a cube whose total
surface area is ( 486 mathrm{cm}^{2} )
9
209Say 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
210If 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
211A 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
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
213Write the formula of curved & total
surface areas of a hemisphere. Also find the ratio between then
9
214The number of vertices in a cube is
( A cdot 6 )
B. 10
( c cdot 8 )
D. 12
9
215If 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
216If the diameter of the base and height of a cylinder are ( 6 mathrm{cm} ) and ( 14 mathrm{cm} ) respectively. Then find its volume.9
217Given 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
218If 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
219There 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
220A 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
221In given figure of cube and cuboid, which one has a greater surface area?
A. cube
B. Cuboid
c. cant compose
D. None
10
222A 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
223A 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
224A 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
225If 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
226Find 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
227The largest sphere is curved out of cube
of side ( 14 c m ). Find surface area of
sphere
9
228A 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
229A 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
230A 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
232The 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
233Find the total volume of these three
identical toy blocks
10
234A 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
235If 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
236The 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
237If 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
238A 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
239How 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
240A 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
241Find the total surface area of a
hemisphere of radius ( 3.5 mathrm{cm} )
9
242Evaluate ( int frac{boldsymbol{d} boldsymbol{x}}{sqrt{(boldsymbol{x}-boldsymbol{alpha})(boldsymbol{beta}-boldsymbol{x})}}, boldsymbol{beta}>boldsymbol{alpha} )9
243A 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
244A 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
245A 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
246Find 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
247The 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
248Find the volume of a sphere whose
( mathbf{0 . 6 3} boldsymbol{m} )
9
249A 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
250If 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
251The 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
25272. 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
253Find 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
254A 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
255The 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
256The 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
257A 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
258A 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
259How 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
260An 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
261Say 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
262Choose the correct answers from the
alternatives given.

If a cone, a hemisphere and a cylinder stand on the same base and have
height equal to the radius of the base, find out the ratio of their volumes.
A . 1: 3: 2
B. 2:3:
c. 3: 2:
D. 1::::

10
263The 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
26466. 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
265A 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
266A 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
267Find the total surface area of cubes
having the following sides.
( 6.8 m )
9
268How 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
269The 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
270Calculate 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
271If the surface area of a hemisphere is ‘S
then express ‘ ( r^{prime} ) in terms of ‘ ( S ) ‘.
9
2723 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
273A 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
274The 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
275If 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
276The 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
277The 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
278A metallic sphere ( 1 mathrm{cm} ) in diameter is beaten into a circular sheet of uniform
thickness equal to 1 mm. Find the
10
279Find the surface area of a sphere of
diameter:
( mathbf{3 . 5} mathrm{cm} )
9
10cm is melted and small lead
The total number of possible
small lead balls is (Take it =
22
7)
(1) 8000
(3) 800
(2) 400
(4) 125
10
281Find the surface area of a sphere of
9
282A 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
283if the total surface area of a solid
hemisphere is ( 462 mathrm{cm}^{2} ) find its volume
9
284Find the volume of the sphere whose
curved surface area is ( 616 mathrm{cm}^{2} )
9
285If 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
286Find the total surface area of a cube
with side ( 5 mathrm{cm} )
9
287Find the volume of largest sphere
covered out of a cube of side ( 7 mathrm{cm} )
10
288If 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
289The 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
290Find the volume of sphere whose radius
is ( 3 mathrm{cm} )
9
291Each 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
292The 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
293A 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
294The 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
295A 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
296An 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
297Find 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
298A 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
299Liquid 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
300The volume of cylinder if the base area
is ( 20 c m^{2} ) and height is ( 5 c m )
9
301Find 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
302Eight 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
303Calculate 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
304The 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
305The height of the cylinder of maximum volume that can be inscribed in a
A ( cdot frac{2 R}{3} )
в. ( frac{R}{3} )
c. ( frac{2 R}{sqrt{3}} )
D. ( frac{R}{sqrt{3}} )
9
306A 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
307STATEMENT – 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
cube
A. Statement – 1 is True, Statement – 2 is True, Statement 2 is a correct explanation for Statement – 1
B. Statement – 1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement – 1
c. statement – 1 is True, Statement – 2 is False
D. Statement – 1 is False, Statement – 2 is True

9
30827 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
309A 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
310Metal 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
311A 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
312A 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
313The 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
314If 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
315Water 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
316A cuboid with equal length, breadth
and height is called a
10
317Water 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
318A cone, hemisphere and a cylinder stand on the same base and have equal
height. Find the ratio of their:
Volumes.
10
31955. 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
32059.
A conical flask is full of water.
height h. This water is poured into
mr. The height of water in the
2h
(1) 2h
(3) 2h
(2) , m?
19h
m
10
321Diameter of a sphere is ( 28 mathrm{cm} ). Find its
surface area(in ( left.c m^{2}right) )
9
322The 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
323The 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
324The 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
325A 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
326If 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
327A 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
328If 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
329The 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
330Find the volume and surface area of a
sphere of radius ( 6.3 mathrm{cm} )
9
331A 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
332If 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
333Find the volume and surface area of a sphere of radius ( 8.4 mathrm{cm} .left(pi=frac{22}{7}right) )9
334If 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
335A 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
336A 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
337Find the L.S.A of a cuboid whose
dimensions are given by ( 3 m times 5 m times )
( 4 m )
9
338The largest sphere is carved out of a cube of a side ( 7 mathrm{cm} . ) Find the volume of
the sphere.
9
339Find the surface area of a sphere of diameter: ( 21 mathrm{cm} )9
340Three 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
341What 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
342The 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
343Find the amount of water displaced by a solid spherical ball of diameter ( 4.2 mathrm{cm} ) when it is completely immersed in
water
9
344A 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
345The 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
346Find the volume of a sphere whose
(i) ( 7 mathrm{cm} )
(ii) ( 0.63 m )
9
347The 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
348Find 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
349The total surface area of a solid
hemisphere is ( 462 mathrm{cm}^{2} . ) Find its radius.
9
350A 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
35158. 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
352The radius of a sphere is ( 3.5 mathrm{cm} ). Find
the surface area and volume.
9
353A 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
354Find the edge of a cube whose volume is
216 cubic centimetres.
9
355Calculate 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
356A 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
357From 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
358The 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
35956. 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
360Find 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
361The 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
362A 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
363Jabu 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
364A 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
365How 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
366A 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
367The 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
368A 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
369A 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
370A 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
371A 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
372The radius of a wooden hemisphere is
10 cm. What is its volume?

If this hemisphere is curved into a cone
of maximum size, find the volume of the
cone.

10
373The 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
374A 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
smaller cones will be
( A cdot 48 )
B. 18
( c cdot 24 )
D. 36
9
375Find 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
376Find 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
377Water 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
378There 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
379If 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
380If 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
381A 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
382The radius of a sphere increased by 50 percent. By how many per cent did the surface area of the sphere increase?9
383A 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
38456. 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
385Bricks 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
386The 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
387Find 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
388The 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
389A 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
390Three 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
391The diameter of a spherical ball is 21 ( mathrm{cm} . ) How much leather is required to prepare 5 such balls.9
392The 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
393If 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
394A road roller takes 750 complete revolutions to move once over to level a
diameter of a road roller is ( 84 mathrm{cm} ) and
length is ( 1 mathrm{m} )
9
395The 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
396The ( T S A ) of cube ( =726 mathrm{cm}^{2} ) find the
edge.
9
397The 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
398Find the volume of a sphere whose
surface area is ( 154 mathrm{cm}^{2} )
9
399A 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
400From 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
401Volume and surface area of a solid
hemisphere are numerically equal then what is the diameter of hemisphere?
9
402A 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
403If 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
404The 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
405If ( 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
406Show that the height of a closed right
circular cylinder of given volume and least surface area is equal to its
diameter.
9
407A 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
408A 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
409Water 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
410If 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
411If 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
412The 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
413The 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
414Each 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
415Water 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
416A road roller takes 750 complete
revolutions to move once over to level a
diameter of a road roller is ( 84 mathrm{cm} ) and
length is ( 1 mathrm{m} )
9
417The 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
418A 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
419An 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
420en
The capacities of two hemispher-
ical vessels are 6.4 litres and
21.6 litres. The ratio of their in-
(1) 4:9 (2) 16: 81
(3) 2 : 13 (4) 2:3
9
421The 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
422The 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
423The 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
424Three 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
425The 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
42655. 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
427A 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
428If 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
429The 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
430What will happen to the volume of the cube, if its edge is
(a) tripled (b) reduced to one-fourth?
9
431A cube has ( _{text {the }} ) egdes
vertices
9
432The 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
433Two cubes each with ( 12 mathrm{cm} ) are joined
end to end. Find the surface area of the
resulting cuboid.
9
434Find the later surface area and total
surface area of the following right
prisms.
9
435A 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
436A 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
437If 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
438The 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
439The 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
440A 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
441A rectangular room is ( 6 m ) long, ( 5 m )
wide and ( 4 m ) high. Find the total surface area of the four walls.
9
442Cylinder ( 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
9
443A 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
444Find the ( T . S . D ) of a cube, whose volume
is ( 3 sqrt{3} a^{3} ) cubic units.
9
445A 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
446Curved 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
447If 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
448The 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
449The 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
450Two 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
451A 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
452Find 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
453A sphere has volume ( 36 pi c m^{3} ), find the
A ( .4 mathrm{cm} )
B. 3 cm
( c .6 c m )
D. 8 ст
9
454How many cubic metres of earth must
be dug to make a well 14 metres deep and 4 metres in diameter?
9
455Find the volume of cylinder, if the radius
of its base is ( 1.5 mathrm{cm} ) and its height is
( mathbf{5} c m )
9
456A 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
457A 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
458The 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
459Find the surface area of a sphere of
diameter:
( mathbf{3 . 5} mathrm{cm} )
9
460It 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
461The vol of a cube ( =1000 mathrm{cm}^{3} ), Find its
TSA in ( c m^{2} )
9
462The 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
463A 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
464Find the surface area of a sphere (in
( c m^{2} ) ) of radius: ( 14 mathrm{cm} )
9
4652 cubes of volumes ( 664 mathrm{cm}^{3} ) are joined
end to end. Fin the surface area of the
reacting cuboid.
9
466The 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
467The 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
468A 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
469A 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
470The 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
471The 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
472The 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
473A 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
474The 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
475Assertion
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
476Find the volume of a sphere of radius
( 2.1 mathrm{cm}left(text { use } pi=frac{22}{7}right) )
9
477The 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
478If the surface area of a sphere is
( 9856 c m^{2} . ) Find its diameter.
A . 28
B. 55
( c .56 )
D. 30
9
479Total 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
480A 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
481The 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
482In 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
483Find 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
484Ps.
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
485Curved 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
486Find 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
487The 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
488The radius of a sphere is ( 2 r, ) then find its
volume
9
489From 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
49059. 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
491If 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
492Water 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
493A 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
494The 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
495The 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
49615 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
497Find the amount of water displaced by a solid spherical ball of diameter
( 0.21 mathrm{cm} )
9
498The 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
49960. 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
500The 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
501Find the volume of a sphere of radius 3
( mathrm{cm} )
9
502The 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
503How many faces a cube has?
A .4
B. 6
c. 8
D. 12
9
504Find 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
505The 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
506A 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
50765. 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
508Which of the following is a unit of Volume?
A. Meters per second
B. Cubic millimeters
c. Litres
D. Both B and C
9
50962. 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
510or 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
511Each 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
512A sphere, cylinder ( & ) a cone gave the same radius ( & ) same height, find the ratio of their curved surface areas.9
513A 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
514State 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
515A 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
516Find 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
517The 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
518Find the total surface of cuboid whose
length is ( 8 c m ) breadth is ( 6 mathrm{cm} ) and
height is ( 5 c m )
10
519How many balls each of radius ( 1 mathrm{cm} )
can be made from a copper sphere whose radius is ( 8 mathrm{cm} ? )
9
520The 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
521Find the volume of a cube if its total
surface area is 294 sq ( c m )
9
522The 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
523Find the volume of hemisphere of
9
524A 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
525Find 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
526An 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
527Find 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
528The 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
529It 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
530A 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
531A 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
532Find the volume of a sphere ( left(operatorname{in} m^{3}right) )
whose diameter is : 2.1 ( mathrm{m} )
9
53359. 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
534The 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
535A 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
536The volume of a cube is ( 1000 mathrm{cm}^{3} ). Find
its total surface area in ( mathrm{cm}^{2} )
9
537The 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
538The 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
539A 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
540Volume 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
A. ( 3 mathrm{cm} )
B. ( 4 mathrm{cm} )
c. ( 4.5 mathrm{cm} )
D. ( 5.5 mathrm{cm} )
9
541A 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
10
542Figure 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
543Consider 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
544A 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
545A 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
546A 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
547The 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
548The 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
549Find 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
550The 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
551Two cubes, each of side ( 4 mathrm{cm} ) are joined end to end. Find the surface area of the
resulting cuboid
9
55261. 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
553Find 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
554The ( 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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