Areas Related To Circles Questions

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

Areas Related To Circles Questions

List of areas related to circles Questions

Question NoQuestionsClass
1A wire is bent in the form of a rectangle having length twice the breadth. The same wire is bent in the form of a
circle. It was found that the area of the
circle is greater than that of the
rectangle by ( 104.5 mathrm{cm}^{2} . ) Find the length of the wire.
10
2sent in the
ses an area
rire is bent
(3) 4010
55. A metal wire when bent in
form of a square encloses an
484 cm. If the same wire is b
in the form of a circle, then ſt
ing n = 2) its area is
(1) 308 cm (2) 506 cm2
(3) 600 cm (4) 616 cm
10
3The long and short hands of a clock are
( 6 mathrm{cm} ) and ( 4 mathrm{cm} ) long respectively. Find the sum of distances travelled by their
tips in 24 hrs. ( (U s e pi=3.14) )
10
4The length and breadth of a rectangle
are in the ratio ( 2: 1 . ) If the area of the
field is 72 sq.m, find the cost of fencing
the field with barbed wire at the ratio of
Rs 15 per metre.
10
5A circular disc of radius ( 7 mathrm{cm} ) has a
sector of angle 45 degrees cut out. The area of the remaining part of the disc is
A ( cdot ) 134.75 ( c m^{2} )
B . ( 144.75 mathrm{cm}^{2} )
c. ( 269.5 mathrm{cm}^{2} )
D. None of these
10
6The area of a circle whose radius is 6
( mathrm{cm} ) is trisected by two concentric circles. The radius of the smallest circle
is
A ( cdot 2 sqrt{3} mathrm{cm} )
B . ( 2 sqrt{6} mathrm{cm} )
( c cdot 2 mathrm{cm} )
D. ( 3 mathrm{cm} )
10
758.
If the radius of a circle is in-
creased by 6%, then its area is
increased by
(1) 15%
(2) 18.46%
(3) 12.36% (4) 20%
10
8Given :
Area of sector ( =15 pi ) sq.cm
radius ( =mathbf{6} c boldsymbol{m} )
To find :
Length of the arc corresponding to the
sector
10
9The radius of a circle with centre 0 is 5
( mathrm{cm} ) (given figure). Two radii OA and ( mathrm{OB} )
are drawn at right angles to each other.
Find the areas of the segment made by the chord ( A B text { (Take } pi=3.14) )
10
10Find the diameter of a circle whose
circumference is equal to the sum of the circumference of the two circles of
diameters ( 36 mathrm{m} ) and ( 20 mathrm{m} )
10
11A wheel has diameters ( 84 mathrm{km} ). Find how
many complete revolution must it take
to cover 792 meters
10
12Four equal circles are described about
four corners of a square so that each
touches two of the others as shown in
the fig. Find the area of the shaded
portion, each side of the square
measuring ( 28 mathrm{cm} )
10
13A rectangular plot is ( 112 mathrm{m} ) long and ( 6 mathrm{m} ) broad. It has ( 2 mathrm{m} ) path all around it on the inside.Find the area of the path and
the cost of constructing it at the rate of
Rs 60 per sq ( m )
10
14A swimming pool is ( 20 m ) in length, ( 15 m ) in breadth, and ( 4 m ) in depth. Find
the cost of corner its floor and walls at
the rate of ( R s .12 ) per square meter
10
15The difference between the
circumference and the radius of a circle
is ( 74 mathrm{cm}, ) find the area of the circle.
10
16A sphere with diameter ( 50 mathrm{cm} )
intersects a plane ( 14 mathrm{cm} ) from the center of the sphere. What is the
number of square centimeters in the area of the circle formed?
A . ( 49 pi )
в. ( 196 pi )
c. ( 429 pi )
D. ( 576 pi )
E . ( 2304 pi )
10
17A circle and a squre have the same
perimeter. Then:
A. there areas are equal
B. the area of the circle is the greater
C. the area of the square is the greater
D. the area of the circle is ( x ) times the area of the square
E. none of these
10
18n figure, circle ( O ) has diameter ( overline{A B} ) of
the length ( 8 . ) If smaller circle ( P ) is
( operatorname{tangent} ) to diameter ( overline{A B} ) at point ( O ) and
is also tangent to circle ( O ), calculate the
approximate area of the shaded region.
A . 3.14
B. 6.28
( c .9 .42 )
D. 12.57
E . 25.13
10
19How to find area of circle?10
20The radius of a semi-circular plot is 21
m. Find its area and perimeter.
10
21Find the area of both the segments of a
Circle of radius ( 43 mathrm{cm} ) with central angle ( 120^{circ} .left[text { Given, } sin 120^{circ}=frac{sqrt{3}}{2} a n d sqrt{3}=right. )
1.73]
10
22In the given figure the diameter of the biggest semi circle is ( 56 mathrm{cm} ) and the
radius of the smallest circle is ( 7 mathrm{cms} )
The area of the shaded portion is
A ( cdot 482 mathrm{cm}^{2} )
B. ( 462 mathrm{cm}^{2} )
( mathbf{c} cdot 654 mathrm{cm}^{2} )
D. ( 804 mathrm{cm}^{2} )
10
23Find the sum of the perimeters of the
figures given below
A. ( 350 mathrm{cm} )
B. 360 cm
c. ( 370 mathrm{cm} )
D. ( 380 mathrm{cm} )
10
24The area of a circle is the measurement
of the region enclosed by its
A . radius
B. centre
c. circumference
D. area
10
25Area of square is 10,000 sq m Then its side measures(in ( mathrm{m}) )10
26A circle is inscribed in a square and
then a smaller square is inscribed in the circle. The ratio of the area of the
smaller square to that of the larger square is
A . 1: 4
B. ( sqrt{2}: 2 )
( c cdot 1: 2 )
D. ( 1: sqrt{2} )
E . 2: 3
10
27In Figure ( 5, ) rectangle ( A B C D ) is
inscribed in a circle. If the radius of the
circle is 1 and ( A B=1 ), find the area of
the shaded region.
( mathbf{A} cdot 0.091 )
B. 0.285
c. 0.614
D. 0.705
E . 0.732
10
28If the radius of a circle is tripled, the
ares becomes.
A. 9 times
B. 3 times
c. 6 times
D. 30 times
10
29Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius ( 5 mathrm{m} ) drawn in a park.
Reshma throws a ball to Salma. Salma
to Mandip, Mandip to Reshma. If the distance between Reshma and Salma
and between Salma and Mandip is ( 6 mathrm{m} ) each, what is the distance
between Reshma and Mandip?
( mathbf{A} cdot 4.8 mathrm{m} )
B. ( 9.6 mathrm{m} )
( c cdot 2.4 m )
D. ( 7.2 mathrm{m} )
10
30Find the area of a sector in radians
whose central angle is ( 45^{circ} ) and radius is
2
A ( cdot frac{pi}{3} )
в.
( c cdot frac{pi}{2} )
D.
10
31In the figure 7.31 , radius of the circle is
( mathbf{7} boldsymbol{c m} ) and ( boldsymbol{m}(boldsymbol{a} boldsymbol{r} boldsymbol{c} boldsymbol{M} boldsymbol{B} boldsymbol{N})=boldsymbol{6} boldsymbol{0}^{o} )
find Area of the circle.
A . 45
B . 42.96
c. 43.96
D. 44
10
32If an area enclosed by a circle or a square or an equilateral triangle is the same, then the maximum perimeter is possessed by:
A. the circle
B. the square
c. the equilateral triangle
D. the triangle and square have equal perimeters greater than that of circle
10
33The perimeter of the table.
A ( .402 .60 mathrm{cm} )
B. ( 522.60 mathrm{cm} )
c. ( 342.60 mathrm{cm} )
D. None of these
10
34A piece of land is 100 metres ( times 21 ) metres. A semi-circular plot has been
added on one side of its breadth. How
long will it take a man to walk round it
at the rate of 3.6 kilometres per hour?
10
35A chord ( A B ) of a circle, of radius ( 14 mathrm{cm} )
makes an angle of ( 60^{circ} ) at the centre of
the circle. Find the area of the minor
segments of the circle.
10
36The radius of a wheel is 0.25 m. How
many rounds will it take to complete the distance of ( 11 k m ? )
A. 7000
в. 8000
c. 9000
D. 6000
10
37A chord of a circle radius ( 14 mathrm{cm} ) makes
a right angle at the centre. Find the areas of the minor and major segments of the circle
10
38The area of a square is numerically equal to the perimeter of the square, then the side of square is
A . 2 units
B. 3 units
c. 4 units
D. 5 units
10
39What is the area of the circle whose
equation is ( (x-3)^{2}+(y+5)^{2}=18 ? )
( mathbf{A} cdot 9 pi )
B. ( 18 pi )
c. ( 72 pi )
D. ( 81 pi )
E . ( 324 pi )
10
40How many times a wheel of radius 28 cm must rotate to go 352 m?(Take ( pi= )
( frac{22}{7} )
10
41Abhay made a straight cut through a circular rubber band and then laid the
rubber band flat, as shown in the figure.
Which measure corresponds to the
length of the cut rubber band?
A. Chord
B. Circumference
c. Diameter
D. Radius
10
42If ( A C ) passes through the centre of the
circle, then the area of the shaded
region in the given figure is
A ( cdot frac{a^{2}}{2}(3-pi) )
B ( cdot a^{2}left(frac{pi}{2}-1right) )
( mathbf{c} cdot 2 a^{2}(pi-1) )
( ^{mathrm{D}} cdot frac{a^{2}}{2}left(frac{pi}{2}-1right) )
10
43The perimeters of a circular field and a square field are equal. If the area of the square field is ( 12100 m^{2} ), then the area
of the circular field will be
A. ( 15500 m^{2} )
В. ( 15400 m^{2} )
c. ( 15200 m^{2} )
D. ( 15300 m^{2} )
10
44In Figure ( 5, ) rectangle ( A B C D ) is
inscribed in a circle. If the radius of the
circle is 2 and ( overline{C D}=2, ) find the area of
the shaded region.
A. 0.36
3. 0.47
7
( c .0 .57 )
D. 0.707
( =0.86 )
10
45If the circumference (in ( c m ) ) and the
( operatorname{area}left(operatorname{in} c m^{2}right) ) of a circle are equal then
find the radius of the circle
A . ( 1 c m )
в. 2 ст
( c .3 c m )
D. ( 4 c m )
10
46Let ( C ) and ( A ) be the circumference and
the area of a circle respectively. If ( x C ) is
the circumference of another circle
whose area is ( 2 A ), then ( x ) equals
begin{tabular}{l}
A ( cdot 2 sqrt{2} ) \
hline
end{tabular}
B. 2
( c cdot sqrt{2} )
D. ( frac{1}{2} )
10
47The moon is about ( 384000 mathrm{km} ) from the
earth and its path around the earth is
nearly circular. Find circumference of
the path travelled by the moon every
month.
10
48The area of the part of the square filed in which a horse tied to a fixed pole at
one comer by means of a 10 m rope, can
graze is
A . ( 25 pi s q . m ).
в. ( 100 pi s q . m )
c. ( 50 pi s q . m )
D. ( 5 pi s q . m . )
10
49The diameter of a circle is ( 10 mathrm{cm} . ) Find
the length of the arc, in cm, (nearest integral value), when the
corresponding central angle is ( 45^{circ} )
10
50Calculate the area of the rectangle whose length ( 20 m ) and breadth ( 11 m )10
51A chord ( A B ) of circle of radius ( 14 c m )
makes an angle of ( 60^{circ} ) at the centre of
the circle .The area of the minor
segment of the circle is ( left(text { Use } pi=frac{22}{7}right) )
A ( cdot frac{308}{3} c m^{2} )
в. ( frac{208}{3} mathrm{cm}^{2} )
c. ( frac{108}{3} mathrm{cm}^{2} )
D. ( frac{408}{3} mathrm{cm}^{2} )
10
52If the difference between the
circumference and radius of a circle is
( 37 mathrm{cm}, ) then the area of the circle is
( A cdot 111 mathrm{cm}^{2} )
B. ( 148 mathrm{cm}^{2} )
( c cdot 259 mathrm{cm}^{2} )
D. ( 154 mathrm{cm}^{2} )
10
53A chord of a circle of radius ( 6 mathrm{cm} )
subtends an angle of ( 60^{circ} ) at the centre
of the circle. The area of the minor
segment is (use ( pi=3.14) )
A ( cdot 6.54 mathrm{cm}^{2} )
в. ( 0.327 mathrm{cm}^{2} )
c. ( 7.25 mathrm{cm}^{2} )
D. 3.27 ( c m^{2} )
10
54A sector of a circle of radius ( 8 mathrm{cm} )
contains an angle of ( 135^{circ} . ) Find the area
of the sector.
10
55Which of the following is/are correct?
This question has multiple correct options
A. Area of a circle with radius ( 6 mathrm{cm} ), if angle of sector is ( 60^{circ}, ) is ( frac{132}{14} mathrm{cm}^{2} )
B. If a chord of circle of radius ( 14 mathrm{cm} ) makes an angle of
( 60^{circ} ) at the centre of the circle, then area of major sector is ( 512.87 mathrm{cm}^{2} )
C. The ratio between the circumference and area of a
circle of radius ( 5 mathrm{cm} ) is 2: 5
D. Area of a circle whose radius is ( 6 mathrm{cm} ), when the length
of a arc is ( 22 mathrm{cm}, ) is ( 66 mathrm{cm}^{2} )
10
56Find the area of shaded region?10
57In the given figure two concentric circle
with centre ( O ) have radii ( 21 c m ) and
( 42 c m . ) If ( A O B=60 ) Find the area of the
shaded region (Use ( left.pi=frac{22}{7}right) )
10
5858. The diameters of two circles are
the side of a square and the di-
agonal of the square. The ratio of
the areas of the smaller circle and
the larger circle is
(1) 1 : 2 (2) 1:4
(3) V: V3 (4) 1 : 72
10
59An equilateral triangle and a square have equal perimeters. If side of the triangle is ( 9.6 mathrm{cm} ; ) what is the length of
the side of the square?
( mathbf{A} cdot 6.2 mathrm{cm} )
B. ( 3.2 mathrm{cm} )
( c .5 .2 mathrm{cm} )
D. ( 7.2 mathrm{cm} )
10
60( mathbf{n} )
fig., ( A B ) and ( C D ) are two diameters of ( a )
circle (with centre 0) perpendicular to
each other and 0 D is the diameter of the
smaller circle. If ( boldsymbol{O} boldsymbol{A}=mathbf{1 4} boldsymbol{c m}, ) find the
area of the shaded region
10
61( A, B, ) and ( C ) are three points on a circle
with centre ( boldsymbol{O} ) such that ( boldsymbol{B O C}=mathbf{3 0}^{mathbf{o}} )
and ( angle A O B=60^{circ} . ) If ( D ) is a point on the
circle other than the arc ( A B C ), find
( angle A D C )
( A cdot 45 )
В. 60
( c cdot 22.5^{circ} )
0.30
10
62In a circle of radius ( 21 mathrm{cm}, ) an arc
subtends an angle of ( 60^{circ} ) at the centre.
The area of the segment formed by the corresponding chord of the arc is :
A ( .42 mathrm{cm}^{2} )
В. 421.73 ( c m^{2} )
c. ( 429.43 mathrm{cm}^{2} )
D. ( 40 mathrm{cm}^{2} )
10
63Find the angle subtended at the centre
of the circle by an are whose length is ( 15 mathrm{cm} ) if the radius of the circle is
( mathbf{2 5} mathrm{cm} )
10
64A circle is inscribed in a triangle whose
sides are 40,40 and ( 48 mathrm{cm} ) respectively. A smaller circle touching two equal sides of the triangle and to the first circles, then the area of smaller circle is
10
65The area of the circle whose centre is
(1,2) and which passes through the point (4,6) is
A ( .25 pi )
в. ( 100 pi )
c. ( 92 pi )
D. None of these
10
66The area of the shaded region in the following figure is
A ( .51 .33 mathrm{cm}^{2} )
В. ( 102.67 mathrm{cm}^{2} )
c. ( 205.34 mathrm{cm}^{2} )
D. can not be determined
10
67The diameter of the wheel of a car is
( mathbf{5 6} ) cm. Calculate :
The number of times the wheel will
rotate in travelling through a distance of ( 1.056 k m )
10
68What will be the area of the field
( A B G F E A ? )
( mathbf{A} cdot 7225 m^{2} )
B. ( 8225 mathrm{m}^{2} )
( c cdot 6225 m^{2} )
D. ( 6725 m^{2} )
10
69The perimeter of a square field is ( 40 mathrm{m} ) more than another square field. Three
times the area of the smaller field is 50
( m^{2} ) more than the area of the larger field. Find the sides of both the fields.
10
70A horse is placed for grazing inside a
rectangular field ( 70 m ) by ( 52 mathrm{m} ) and is
tethered to one corner by a rope ( 21 mathrm{m} )
long. On how much area can it graze?
A ( .346 .5 mathrm{cm}^{2} )
В. ( 360 mathrm{cm}^{2} )
c. ( 350.5 mathrm{cm}^{2} )
D. ( 380 c m^{2} )
10
71Parveen wanted to make a temporary shelter for her car, by making box-like structure with tarpoulin 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 ? )
10
72The area of a circle is ( (14+6 sqrt{5}) pi )
units, Find its radius.
10
73If ( A, B, C, D ) are four points such that
( angle B A C=30^{circ} ) and ( angle B D C=60^{circ} ) then
prove that
D is the centre of the circle through ( A, B ) and ( mathrm{C} )
10
74Find the area of the segment AYB shown
in figure, if radius of the circle is ( 21 mathrm{cm} ) and ( <A O B=120^{circ} .left(U s e pi=frac{22}{7}right) )
10
75Find the area of the circle whose centre
is (-3,2) and (2,5) is a point on the circle.
10
76If the length of a rectangle is two times its breadth and area is ( 228 mathrm{cm}^{2} ), then
length and breadth are respectively
A ( .20 mathrm{cm}, 10 mathrm{cm} )
в. ( 12 mathrm{cm}, 24 mathrm{cm} )
c. ( 24 c m, 12 c m )
D. ( 16 mathrm{cm}, 18 mathrm{cm} )
10
77Calculate the arc length for the given
diagram.
A . 1.23 in
B . 2.23 in
c. 4.23 in
D. 5.23 in
10
78A table-top measures ( 2 m 25 mathrm{cm} ) by
1 ( m 50 mathrm{cm} . ) What is the perimeter of the table-top?
10
79Find the radius of the incircle of a
triangle whose sides are 18,24 and 30
10
80A square park has each side of ( 100 m )
At each corner of the park, there is a
flower bed in the form of a quadrant of
radius ( 14 m ) as shown in figure. Find the
area of the remaining part of the park. ( left[text { Use } boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] )
A ( cdot 12843 m^{2} )
B. ( 11284 m^{2} )
( mathrm{c} cdot 9384 m^{2} )
D. ( 7382 m^{2} )
10
81Taking ( boldsymbol{pi}=mathbf{3 . 1 4}, ) find the
circumference of a circle whose radius
is ( 8 mathrm{cm} )
10
82A chord of a circle of radius ( 10 mathrm{cm} )
subtends a right angle at the centre. Find the area of the corresponding
( (i) )
Minor segment,
(ii) Major segment. (use ( boldsymbol{pi}=mathbf{3 . 1 4}) )
10
83Find the area of each of the following
figures.
10
84Find the area of the circular park of
Janakpuri whose circumference is
( 77 m 77 m )
A ( .671 .87 m^{2} )
B. ( 331.62 m^{2} )
( mathbf{c} cdot 471.62 m^{2} )
D ( .401 .62 m^{2} )
10
85In case of a right circular cylinder the radius of base and height are in the ratio ( 2: 3 . ) Therefore, the ratio of lateral
surface area to the total surface area is
A .5: 3
B. 3: 5
c. 2: 5
D. 2: 3
10
86A eighth part of a full circle i.e. a octant subtends an angle of ( ldots ) at the centre.
A ( cdot 60^{circ} )
B . ( 45^{circ} )
( c .90^{circ} )
D. None of these
10
87A chord of a circle of radius ( 10 mathrm{cm} )
subtends a right angle at the centre. Find the area of corresponding minor
segment ( (boldsymbol{pi}=mathbf{3 . 1 4}) )
10
88A square park has each side ( 100 m ). At
each corner of the park there is a flower
bed in the form of a quadrant of radius
( 14 m, ) as shown in the figure. The area of
the remaining part of the park is:
10
89Find the area of the shaded region
( (boldsymbol{pi}=mathbf{3 . 1 4}, sqrt{mathbf{3}}=mathbf{1 . 7 3}) )
10
90n Fig 10.3 if ( mathrm{OA}=5 mathrm{cm}, mathrm{AB}=8 mathrm{cm} ) and
OD is perpendicular to AB then CD is
equal to
( A cdot 2 mathrm{cm} )
B. 3 ( mathrm{cm} )
( c cdot 4 mathrm{cm} )
D
10
91A chord of a circle of radius ( 7 mathrm{cm} )
subtends an angle of ( 90^{circ} ) at its centre. The ratio of areas of smaller and larger
segment is
A .2: 7
B. 1: 10
c. 1: 11
D. none of these
10
92n the given figure, ( A T ) is a tangent
( A C=B C ) and ( angle A B C=50^{circ} . ) Find the
( angle B A T )
10
93A square OABC is inscribed in a
quardrant OPBQ of a circle. If ( O A=21 mathrm{cm} ) find the area of the shaded region.
10
94divides a circle into
two segments i.e major segment and minor segment.
A. An arc
B. A chord
c. A sector
D. A tangent
10
95If the wheel of the bus is ( 90 mathrm{cm} )
diameter makes 210 revolutions per
minute, then find the speed of the bus
in ( k m / h r, ) to the nearest integer.
10
96Find the perimeter of
(i) ( Delta mathrm{ABC} )
(ii) rectangle BCDE.
( mathbf{A} )
(i) ( -8 frac{1}{60} mathrm{cm}, ) (ii)- ( 5 mathrm{cm} )
3
(i) ( -5 c m, ) (ii) ( -10 frac{1}{6} mathrm{cm} )
c. ( left(text { i) }-8 frac{1}{60} text { cm, (ii) }-10 frac{1}{5} ) cm right.
) . (i)- ( 8 mathrm{cm}, ) (ii) ( -23 mathrm{cm} )
10
97If the diameter of a circle is increased
by ( 200 % ) then its area is increased by
A. ( 100 % )
B . 200%
c. 300%
D. 800%
10
98The given figure is made up of identical
squares. Find the area of the shaded
region.
( A cdot 50 mathrm{cm}^{2} )
B. ( 54 mathrm{cm}^{2} )
( mathrm{c} cdot 58 mathrm{cm}^{2} )
D. ( 52 mathrm{cm}^{2} )
10
99( Delta L M N Delta L M N )
(2) Area of any one of the sectors.
(3) Total area of all the three sectors.
(4) Area of the shaded region.
10
100Find the area of the minor segment of a circle of radius ( 14 mathrm{cm}, ) when its central angle is ( 60^{circ} ). Also find the area of the
corresponding major segment. ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] )
10
101If the difference between the
circumference and the radius of a circle
is ( 37 c m, ) then using ( pi=frac{22}{7}, ) the
circumference (in cm) of the circle is:
A . 154
B. 44
c. 14
D.
10
102In figure, square ( J K L M ) is inscribed in
circle ( O . ) If the radius is ( 6, ) calculate the
area of the shaded region, to the nearest
tenth.
A . 10.3
B. 18.2
c. 22.8
D. 28.3
E . 38.6
10
103Find the diameter of a circle whose
circumference is ( 15.7 mathrm{cm}- )
A. ( 5 mathrm{cm} )
B. ( 6 mathrm{cm} )
( c cdot 7 mathrm{cm} )
D. 4.5 cm
10
104Find the area of a triangle, two sides of
which are ( 8 mathrm{cm} ) and ( 11 mathrm{cm} ) and the
perimeter is ( 32 mathrm{cm} )
10
105The diameters of the front and the rear
wheels of a tractor are ( 63 mathrm{cm} ) and
1.54 ( m ) respectively. Calculate their areas and circumference.
10
106An equilateral triangle has area ( A sqrt{3} ) Three circles are drawn with their
centres at the vertices of the triangle. Diameter of each circle is equal to the
length of each side of the triangle. The area of the triangle NOT included in any
of the three circles is
A ( cdot Aleft(sqrt{3}-frac{pi}{6}right) )
B . ( A(pi-sqrt{3}) )
c. ( A(3 pi-sqrt{3}) )
D. ( Aleft(sqrt{3}-frac{pi}{2}right) )
10
107In the fig., ( O A B C ) is a square inscribed
in a quadrant ( O P B Q . ) If ( O A=20 mathrm{cm} )
Find the area of shaded region.
( [boldsymbol{pi}=mathbf{3 . 1 4}] )
10
108The perimeter of a square is ( 56 mathrm{m} ). The
area of rectangle is 8 sq.m less than the
area of the given square. If the length of the rectangle is ( 16 mathrm{m} ), find its breadth.
10
109The diameter of a circle is ( 1 . ) Calculate
the area of the circle.
A ( cdot frac{pi}{8} )
B.
c.
D. ( pi )
E . ( 2 pi )
10
110A chord of a circle of radius ( 12 mathrm{cm} )
subtends an angle of ( 120^{circ} ) at the centre.
Find the area of the corresponding
segment of the circle. (Use ( pi=3.14 text { and } sqrt{3}=1.73) )
10
111In a circle a central angle of ( 60^{circ} )
intercepts an arc of 15 inches. How many inches is the radius of the circle?
A ( cdot frac{45}{pi} )
в.
( c cdot 4 )
D. ( frac{2 pi}{3} )
E. not computable from given data
10
112In Fig. arcs have been drawn of radius
( 21 mathrm{cm} ) each with vertices ( A, B, C ) and ( D )
of the square ( A B C D ) as centres. The
area of the shaded region is
( mathbf{A} cdot 693 mathrm{cm}^{2} )
B. ( 346.5 mathrm{cm}^{2} )
( mathbf{c} cdot 2772 mathrm{cm}^{2} )
D. ( 1386 mathrm{cm}^{2} )
10
113The radii of two circle are ( 4 mathrm{cm} ) and 3
( mathrm{cm} ) respectively, The diameter of the circle having area equal to the sum of the areas of the two circles(in cm) is
A . 5
B. 7
c. 10
D. 14
10
11467. If the circumference of a circle
30
is
7
the the diameter of the
circle is
15
2
(1)
(3) 60
(2) 2
(4) 30
10
115From a circle with radius ( 21 mathrm{cm} ) a
sector is cut off for which the measure
of the angle at the centre is ( 150 . ) Find
the length of the arc of that sector and
also find the area of the sector.
10
116The area of a circle is 314 sq. ( mathrm{cm} ) and area of its minor sector is 31.4 sq. cm.
Find the area of its major sector.
A ( .282 .6 mathrm{cm}^{2} )
в. ( 200.6 mathrm{cm}^{2} )
( mathbf{c} cdot 180.04 mathrm{cm}^{2} )
D. 1220.09cm ( ^{2} )
10
117The diagram shows two arcs, A and B.
Arc A is part of the circle with centre 0 and radius OP. Arc B is part of the circle
with centre ( mathrm{M} ) and radius PM, where M is
the mid – point of PQ. Show that the area
enclosed by the two arcs is equal to 25 ( left(sqrt{3}-frac{pi}{6}right) c m^{2} )
10
118Find the perimeter and area of semicircles(Half cut rings) whose diameters are
¡) ( 2.8 mathrm{cm} )
ii) ( 56 mathrm{cm} )
iii) ( 84 mathrm{cm} )
iv) ( 112 mathrm{cm} )
10
119Find the area of the given figure.10
120Calculate the area of the designed
region in Fig. common between the two
quadrants of circles of radius ( 8 mathrm{cm} )
each
10
121The longest rod that can be placed flat on the bottom of a box is ( 45 mathrm{cm} ). The box
is ( 8 mathrm{cm} ) longer than it is wide. Find the
length and breadth of the box.
10
122The number of marble slabs of size
( 20 mathrm{cm} times 30 mathrm{cm} ) required to pave the
floor of a square room of side 3 metres
is
A. 100
в. 150
( c .225 )
D. 25
10
123( A ) took 15 seconds to cross a
rectangular field diagonally walking at the rate of ( 52 mathrm{m} / mathrm{min} ) and ( mathrm{B} ) took the
same time to cross the same field along
its sides, walking at the rate of 68 ( mathrm{m} / mathrm{min.} ) The area of the field is:
A ( cdot 30 m^{2} )
в. ( 40 mathrm{m}^{2} )
( mathbf{c} cdot 50 m^{2} )
D. ( 60 m^{2} )
10
124In the given figure, ( O ) is the centre of the
circle, ( angle A C B=54^{circ} ) and ( B C E ) is a
straight line. Find ( boldsymbol{x} )
( A cdot 126 )
B. 54
( c cdot 108 )
D. 90
10
125Area of a sector having radius ( 12 mathrm{cm} ) and arc length ( 21 mathrm{cm} ) is
A ( cdot 126 ~ c m^{2} )
B. ( 252 mathrm{cm}^{2} )
( mathrm{c} cdot 33 mathrm{cm}^{2} )
D. ( 45 mathrm{cm}^{2} )
10
126A piece of wire ( 22 mathrm{cm} ) long is bent into the form of an arc of a circle subtending an angle of ( 60^{circ} ) at its center. Find the radius of the circle ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] )10
127In the given figure, ( O ) is the centre of the
circle and ( angle Q P R=x^{circ} ; angle O R Q=y^{circ} )
Which statement is true about ( x^{circ} ) and
( boldsymbol{y}^{circ} ? )
A ( cdot x^{circ}+y^{circ}=120^{circ} )
В . ( x^{circ}+y^{circ}=180^{circ} )
c. ( x^{circ}+y^{circ}=90^{circ} )
D. ( x^{circ}+y^{circ}=150^{circ} )
10
128If the area of a semicircle is ( 84 mathrm{cm}^{2} )
then the area of the circle is
A ( cdot 144 mathrm{cm}^{2} )
B. ( 42 mathrm{cm}^{2} )
( mathbf{c} cdot 168 mathrm{cm}^{2} )
D. ( 288 mathrm{cm}^{2} )
10
129Area of a square 625 sq m Then the measure of its side is
A. ( 15 mathrm{m} )
B. 25
( c cdot 20 m )
D. 24
10
130If the perimeter of a circle is ( 132 mathrm{cm} )
find its area.
A. 1356 sq. ( mathrm{cm} )
B. 1386 sq. ( mathrm{cm} )
c. 1340 sq. ( mathrm{cm} )
D. 1436 sq. ( mathrm{cm} )
10
131Two arcs of the same circle have their
lengths in the ratio ( 4: 5 . ) Then the ratio of the areas of the corresponding sectors is 4: 5
If true then enter 1 and if false then
enter 0
( A )
10
132Find the radius of the circle whose
circumference is ( 44 mathrm{cm} .(pi=22 / 7) )
10
133In a circular table corner of radius
( 32 mathrm{cm}, ) a design is formed leaving an
equilateral triangle ( A B C ) in the middle as shown in Fig. Find the area of the design
10
134Find the area of the shaded segment(in
sq. units)
( A cdot 88.5 )
3,90,5
( c .86 .5 )
88
10
135Find the area of a segment of a circle
with a central angle of 135 degrees and a radius of 2. Express answer to nearest integer.
A . 1
B . 2
( c .3 )
( D )
10
136The difference between the semi
perimeter and the side of a ( Delta A B C ) arre 8 ( mathrm{cm}, 7 mathrm{cm} ) and ( 5 mathrm{cm} ) respectively. Find the area of the triangle
10
137The area of the top of the table
( mathbf{A} cdot 8478 mathrm{cm}^{2} )
B ( .65478 mathrm{cm}^{2} )
( c cdot 7678 c m^{2} )
D. None
10
138Two circles touch internally. The sum of their areas is ( 116 pi ) sq. ( mathrm{cm} ) and the
distance between their centers is ( 6 mathrm{cm} )
The radii of the given circles are
A. ( 8 mathrm{cm} & 20 mathrm{cm} )
B. ( 4 mathrm{cm} & 10 mathrm{cm} )
c. ( 6 mathrm{cm} ) & ( 8 mathrm{cm} )
D. ( 5 mathrm{cm} ) & ( 9 mathrm{cm} )
10
139What is the area of the shaded
segment?
( A cdot 1 m^{2} )
3. ( 2 m^{2} )
( c cdot 3 m^{2} )
D. ( 4 mathrm{m}^{2} )
10
140If the circumference of a circle exceeds
its diameter by ( 30 mathrm{cm}, ) find the radius of the circle.
10
141Calculate the area of a segment of a
circle with a central angle of 165 degrees and a radius of ( 4 . ) Express answer to nearest integer.
A . 10
B . 20
c. 30
D. 40
10
142Fill in the Blank:
Two units Area:
(a)
( (b) )
10
143In the figure, PR and QS are two
diameters of the circle.
If ( P R=28 c m ) and ( P S=14 sqrt{3} mathrm{cm} )
then find the total area of two shaded
segments. ( (sqrt{3}=1.73) )
A ( cdot 249,12 mathrm{cm}^{2} )
B . ( 240.76 mathrm{cm}^{2} )
c. ( 251.12 mathrm{cm}^{2} )
D. None of these
10
144A circle of ‘a’ radius is divided into 6
equal sectors An equilateral triangle is drawn on the chord of each sectors to lie
outside the circle. The area of the
resulting figure is
10
145Find the area of a sector with an arc
length of ( 20 c m ) and a radius of ( 6 mathrm{cm} )
( mathbf{A} cdot 20 mathrm{cm}^{2} )
B. ( 40 mathrm{cm}^{2} )
( c cdot 60 c m^{2} )
D. ( 80 mathrm{cm}^{2} )
10
146The radii of two circles are ( 8 mathrm{cm} ) and
( 6 mathrm{cm} ) respectively. Find the radius of the
circle having area equal to the sum of the areas of the two circles
10
147A chord of a circle of radius ( 6 mathrm{cm} )
subtends a right angle at centre. The area of the minor segment ( (pi=3.14) )
is
A ( cdot 9.82 mathrm{cm}^{2} )
B. ( 10.14 mathrm{cm}^{2} )
c. ( 10.26 mathrm{cm}^{2} )
D. ( 12.35 mathrm{cm}^{2} )
10
148A man walks in a horizontal circle round
the foot of a pole which is inclined to the
vertical. The foot of the pole is at the
centre of the circle. The greatest and least angles which the pole subtends at his eye are ( tan ^{-1}left(frac{9}{5}right) ) and ( tan ^{-1}left(frac{6}{5}right) )
respectively and when he is midway between the corresponding positions, the angle is ( theta ). If the man’s height be neglected, find the length of the pole.
10
149The circumference of the front wheel of
a cart is ( 30 mathrm{ft} ) long and that of the back wheel is 36 ft long. What is the distance travelled by the cart when the front wheel has done five more revolutions
than the rear wheel?
A ( .20 f t )
B. 25 ft
c. ( 750 f t )
D. ( 900 f t )
10
150Sonali pounded a stake into the ground, when she attached a rope to both the stake and her dog’s collar, the dog could reach 9 feet from the stake in any direction. Find the approximate area of the lawn, in square feet, the dog could
reach from the stake. ( (pi=3.14) )
A . 28
B. 57
( c .113 )
D. 254
10
151The area of an equilateral triangle of
side ( 13 mathrm{cm}, ) is
A. 74.079 sq.cm
в. 76.719 sq.cm
c. 63.917 sq.cm
D. 73.179 sq.cm
10
152A horse is tied to a peg at one corner of
a square shaped grass field of side ( 15 m )
by means of a ( 5 m ) long rope. Find
(i) the area of that part of the field in
which the horse can graze.
(ii) The increase in the grazing area if
the rope were ( 10 m ) long instead of ( 5 m )
(Use ( boldsymbol{pi}=mathbf{3 . 1 4}) )
10
153A boy is running around a rectangular
park, whose sides are in the ratio of 4
( 3, ) at the rate of 10 metre per second
and completes a round in 42 seconds. Calculate the area of the park.
10
154A square and a regular hexagon have equal perimeters. Their areas are in the
ratio:
A .2: 1
B. ( 2 sqrt{3}: 1 )
c. ( sqrt{3}: 2 )
D. 3: 2
10
155A chord of radius ( 12 mathrm{cm} ) subtends an
angle of ( 120^{circ} ) at the centre. Find the
area of corresponding segment of the circle. ( (22 / 7=3.14 text { and } operatorname{root} 3=1.73) )
10
15657. The wheel of a motor car makes
1000 revolutions in moving 440
m. The diameter (in metre) of the
wheel is
(1) 0.44 (2) 0.14
(3) 0.24 (4) 0.34
10
157The diameter of a wheel is 1.26 m. How
far will it travel in 500 revolutions?
( mathbf{A} cdot 1980 m )
B. 2000m
( c .2420 m )
D. ( 1890 m )
10
158A wire is in the shape of a square of side ( 10 mathrm{cm} . ) If the wire is rebent into a
rectangle of length ( 12 mathrm{cm} ), find its breadth. Which figure encloses more area and by how much?
10
159Find the circumference of the circle
whose radius is ( 28 mathrm{mm} . ) Take ( pi=frac{22}{7} )
10
160In the following figure, the radius of the
circle is ( 7 mathrm{cm} ) and ( m(a r c R Y S)=30^{circ} )
find find:
Area of the circle
10
161Find the area of a circle whose
circumference is ( 484 mathrm{cm} )
10
162Write the formulae of area and volume
of different solid shapes. Find out the variables and constants in them
10
163n Fig., ( A B ) and ( C D ) are two diameters
of a circle with centre ( O, ) which are
perpendicular to each other. ( boldsymbol{O B} ) is the
diameter of the smaller circle. If ( boldsymbol{O A}= )
( mathbf{7} mathrm{cm}, ) find the area of the shaded region. ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] )
( mathbf{A} cdot 60.5 mathrm{cm}^{2} )
B . ( 63.5 mathrm{cm}^{2} )
( mathbf{c} cdot 66.5 mathrm{cm}^{2} )
D. ( 56.5 mathrm{cm}^{2} )
10
164The area of the shaded region in the diagram below where the given triangle is isoceles with vertices of base lying on
axis of the radius perpendicular to the diameters of the two small semicircles,
is
в. ( 16(pi-1) )
c. ( 32(pi-1) )
D. ( 32(pi+1) )
10
165A steel wire when bent in the form of a
square encloses an area of ( 121 mathrm{cm}^{2} . ) If
the same wire is bent in the form of a
circle, find the area of the circle.
10
166A chord of a circle of radius ( 12 mathrm{cm} )
subtends an angle of ( 60^{circ} ) at the centre.
Find the area of the corresponding segment of the circle. (Use ( pi=3.14 )
and ( sqrt{mathbf{3}}=mathbf{1 . 7 3} )
A ( cdot 17.43 mathrm{cm}^{2} )
B. ( 13.08 mathrm{cm}^{2} )
( mathbf{c} cdot 11.66 mathrm{cm}^{2} )
D. ( 9.64 c m^{2} )
10
167The perimeter of a rectangle is ( 130 mathrm{cm} ) If the breadth of the rectangle is ( 30 mathrm{cm} )
find its length. Also find the area if the
rectangle.
10
168AOBCA is a quadrant of a circle of
radius ( 3.5 mathrm{cm} ) with centre ( 0 . mathrm{P} ) is adjoint
on OB such that ( O P=2 c m ). The area of
the shaded part is
A ( cdot 12.25 mathrm{cm}^{2} )
8. ( 6.125 mathrm{cm}^{2} )
( c cdot 12.5 mathrm{cm}^{2} )
D. None of thes
10
169The diameter of a circle whose area is
equal to the sum of the areas of the two
circles of radii ( 24 mathrm{cm} ) and ( 7 mathrm{cm} ) is
( mathbf{A} cdot 31 mathrm{cm} )
B. ( 25 mathrm{cm} )
( c cdot 62 mathrm{cm} )
D. ( 50 mathrm{cm} )
10
170The diameter of a wheel is ( 2.8 m . ) How
far will travel in 1000 revolution?
10
171Radius of the circular garden is
9.1 metre. What is the ( operatorname{cost}(text { in } R s) ) of
preparing lawn in it at the rate of Rs.100 per 1 sq metre? ( left(pi=frac{22}{7}right) )
10
1722. The perimeter of a sheet of pa-
per in the shape of a quadrant of
a circle is 75 cm. Its area would
(1) 100 cm2
(3) 693 cm
(2) 346.5 cm2
(4) 512.25 cm2
10
173The distance between the two parallel chords of length ( 8 mathrm{cm} ) and ( 6 mathrm{cm} ) in a circle of diameter ( 10 mathrm{cm} ) if the chords lic
on the same side of the centre is
A. ( 1 mathrm{cm} )
B. 2 ( mathrm{cm} )
( c cdot 3 mathrm{cm} )
D. ( 4 mathrm{cm} )
10
174The radius of a circular plot is ( 56 mathrm{m} ). How much will it cost to fence the plot with 4 rounds of wire at the rate of Rs. 40 per meter ?10
175Find the area of the shaded region in
figure ,if ( mathrm{PQ}=24 mathrm{cm}, mathrm{PR}=7 mathrm{cm} ) and ( mathrm{O} ) is
the centre of the circle.
A ( cdot 100.98 mathrm{cm}^{2} )
B ( cdot 161.54 mathrm{cm}^{2} )
c. ( 101.54 mathrm{cm}^{2} )
D. None of these
10
176Illustration 2.23 If arcs of same length in two circles
subtend angles of 60° and 75° at their centers, find the ratios
of their radii.
10
177The area of a circular field is ( 13.86 m^{2} )
Find the circumference of the field.
10
178Two triangular walls of a flyover have been used for advertisements from both
sides. The sides of each wall are ( 120 mathrm{m} )
( 110 mathrm{m} ) and ( 20 mathrm{m} . ) The advertisements
yield an earning of R.s 100 per ( m^{2} ) per
year. Find the amount of revenue earned
in one year. (Take ( sqrt{7}=2.65) )
A. Rs. 3,97,500
B. Rs. 3,47,500
c. Rs. 5,73,300
D. Rs. 4,73,500
10
179The diameter of the moon is
approximately on fourth of the diameter of the earth. Find the ratio of their
surface areas.
10
180Find the length of the side of a square whose area is 441 sq.m.10
181In a circle of radius ( 6 mathrm{cm}, ) a chord of
length ( 10 mathrm{cm} ) makes an angle of ( 110^{circ} mathrm{at} )
the centre of the circle. Find the
circumference of the circle.
10
182In fig two circular flower bds have been
shown on two sides of a lawn ( A B C D ) of
side ( 56 mathrm{m} ). If the centre of each circular
flower bed is the point of intersection ( boldsymbol{O} )
of the diagonals of the square lawn, find
the sum of the areas of the lawn and
flower beds
( mathbf{A} cdot 4032 m^{2} )
B . ( 4428 mathrm{m}^{2} )
( mathbf{c} cdot 4628 m^{2} )
D. None of these
10
183The sum of circumference and the
radius of a circle is ( 51 mathrm{cm} ), find the radius of the circle.
10
184The area of a circle is equal to the area
of a rectangle with sides ( 112 mathrm{m} ) and ( 88 mathrm{m} ) respectively. Find the circumference of the circle.
10
185The perimeter of the following shaded
portion of the figure is
( A cdot 40 mathrm{m} )
В. 40.07 m
( c . ) 35.72m
D. 35
10
186The cost of fencing a circular field at the
rate of ( R s .24 ) per meter is ( R s .5280 /- ) The field is to be ploughed at the.
10
187The perimeter of a rectangle having area equal to ( 144 mathrm{cm}^{2} ) and sides in the
ratio 4: 9
10
188A wire in the shape of an equilateral
triangle encloses an area of ( s mathrm{cm}^{2} ). If
the same wire is bent to form a circle,
then the area of the circle will be
A ( cdot frac{pi s^{2}}{pi} )
B. ( frac{3 s^{2}}{pi} )
( c cdot frac{3 s}{pi} )
D. ( frac{3 s sqrt{3}}{pi} )
10
189Find the area of the sector of a circle
with radius ( 4 mathrm{cm} ) and of angle ( 30^{circ} ). The
answer is ( frac{x n}{3} ) then ( x= )
10
190The area of a quadrant of a circle whose
circumference is ( 44 mathrm{cm} ) is
A ( cdot 144 mathrm{cm}^{2} )
В. ( 175.76 mathrm{cm}^{2} )
c. ( 38.5 mathrm{cm}^{2} )
D. ( 154 mathrm{cm}^{2} )
10
191In the coordinate plane, a circle has center (2,-3) and passes through the point ( (5,0), ) What is the area of the circle?
( A cdot 3 pi )
B. ( 3 sqrt{2} pi )
c. ( 3 sqrt{3} pi )
D. ( 9 pi )
E . ( 18 pi )
10
192Find the difference of the areas of two
segments of a circle formed by a chord of length ( 5 mathrm{cm} . ) Subtending an angle of
( 90^{circ} ) till the centre.
A. 32.14 sq. ( mathrm{cm} )
в. 35.42 sq. ( mathrm{cm} )
c. 38.96 sq. ( mathrm{cm} )
D. 42.43 sq. ( mathrm{cm} )
10
193A chord of a circle of radius ( 15 mathrm{cm} )
subtends an angle of ( 60^{circ} ) at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use ( pi=3.14 text { and } sqrt{3}=1.73) )
10
194How many time will the wheel of a can
rotation in a iorrney of ( 88 mathrm{km} ), given that the diameter of the wheel is ( 56 mathrm{cm} ) ?
10
195A cow is tied to a pole, fixed to the
midpoint of a side of a square field of dimensions ( 40 m times 40 m ), by means of
( 14 m ) long rope. Find the area that the
cow can graze.
A ( .254 m^{2} )
в. ( 308 m^{2} )
c. ( 245 mathrm{m}^{2} )
D. ( 380 m^{2} )
10
196The area ( in square unit) of the circle which touches the lines ( 4 x+3 y=15 )
and ( 4 x+3 y=5 ) is ( m pi . ) Find ( m )
10
197In the following figure, the radius of the
circle is ( 7 mathrm{cm} ) and ( m(a r c R Y S)=30^{circ} )
find find:
( boldsymbol{A}(boldsymbol{P} boldsymbol{R} boldsymbol{X} boldsymbol{S}) )
10
198A circular wire of radius ( 42 mathrm{cm} ) is cut
and bent it into the form of rectangle whose sides are in the ratio of ( 6: 5 . ) The
smaller side of the rectangle is
( A .30 mathrm{cm} )
B. ( 60 mathrm{cm} )
( c .72 mathrm{cm} )
D. ( 132 mathrm{cm} )
10
199Determine the area of the shaded
segment
A . 10
B. 11
( c .12 )
D. 13
10
200In the figure, if the ( angle A O B=60^{circ} ) and
radius is ( 12 mathrm{cm} ), then find the area of the
segment ( A X B .(pi=3.14, sqrt{3}=1.73) )
A . 14
B . 13.08
c. 12
D. 3.14
10
201The length of minute hand of a clock is
14cm. Find the area swept by this minute hand in 10 minutes. ( left(pi=frac{22}{7}right) )
10
202To warn ships for underwater rocks, a lighthouse spreads a red coloured light
over a sector of angle ( 80^{circ} ) to a distance
of ( 16.5 k m . ) Find the area of the sea over
which the ships are warned. (Use ( pi= )
3.14)
10
203The perimeter of a quadrant of a circle of radius ( frac{7}{2} mathrm{cm} ) is:
( mathbf{A} cdot 3.5 mathrm{cm} )
B. ( 5.5 mathrm{cm} )
c. ( 7.5 mathrm{cm} )
D. ( 12.5 mathrm{cm} )
10
204The length of a room is ( 5 m, ) breadth is
( 3.5 m ) and height is ( 4 m . ) Find the total
expenditure of whitewashing on the four walls and roof at the rate of 15 per
square meter. (Answer correctly up to 1 decimal place)
10
205The following circular diagrams represents the yield of gram. If the yield
in field-A is 400 kg, then the yield in field-B will be
A. ( 600 mathrm{kg} )
в. ( 800 mathrm{kg} )
c. 900 kg
D. 1200kg
10
206A path ( 2 m ) wide surrounds a circular
pond of diameter ( 40 m ). How many cubic
metres of gravel are required to grave the path to a depth of ( 20 mathrm{cm} ) ?
10
207Find the area of the sector of circle
which substands an angle of ( 150^{circ} ) at the centre, if the radius of the circle is ( 6 mathrm{cm} )
10
208A chord of a circle of radius ( 12 mathrm{cm} )
subtends an angle of ( 120^{circ} ) at the centre.
Find the area of the corresponding segment of the circle. (Use ( pi=3.14 text { and } sqrt{3}=1.73) )
( mathbf{A} cdot 88.44 )
B. 94.88
c. 43.88
D. 54.88
10
209What is the length of arc AB making angle of ( 126^{0} ) at center of radius ( 8 ? )
A . ( 2.6 pi )
в. ( 5.6 pi )
c. ( 7.6 pi )
D. ( frac{1}{2} pi )
10
210The radii of two circles are in the ratio
( 3: 8 . ) If the difference between their
areas is ( 2695 pi mathrm{cm}^{2}, ) find the area of the
smaller circle.
A ( cdot 1386 mathrm{cm}^{2} )
B. ( 1280 mathrm{cm}^{2} )
( mathbf{c} cdot 1187 mathrm{cm}^{2} )
D. ( 1546 mathrm{cm}^{2} )
10
211A wire bent in the form of a circle of
radius ( 42 mathrm{cm} ) is cut and again bent in
the form of a square. The ratio of the
regions enclosed by the circle and the square in the two cases is given by :
A .11: 12
B. 21: 33
c. 22: 33
D. 14: 11
10
212In the following figure, the circle
centered at ( N ) has a radius of ( 4 . ) What is
the area of the shaded region?
( A cdot 3 pi )
B. ( 6 pi )
( c .9 pi )
D. ( 12 pi )
E . ( 16 pi )
10
213A chord PQ of a length 12 cm subtends
an angle of ( 120^{circ} ) at the center of a circle
Find the area of the minor segment cut
off by chord PQ.
10
214In given fig. of sector of circle of radius
( 10.5 mathrm{cm} . ) What is the perimeter of
sector?
10
215In the given figure, ABCD is a trapezium
of area ( 24.5 c m^{2} . ) If ( A D | )
( boldsymbol{B C}, angle boldsymbol{D A B}=mathbf{9 0}^{0}, boldsymbol{A D}= )
( 10 c m, B C=4 c m ) and ( A B E ) is
quadrant of circle then find the area of
the shaded region.
10
216A horse is tied to a post by a rope If the horse moves along a circular path always keep the rope tight and describes 88 metres when it has traced
out ( 72^{circ} ) at the center, then the length of
rope is
( A cdot 60 m )
B. ( 65 m )
( c .70 m )
D. ( 72 m )
10
217In the given figure 0 is the centre of
circle of radius ( 28 mathrm{cm} . ) Find the area of
the minor segment ASB
10
218Find the area of the segment of circle, given that the angle of the sector is
( 120^{circ} ) and the radius of the circle is
( 21 mathrm{cm} .(text { Take } pi=22 / 7) )
10
219ABCD is a flower bed. If ( O A=21 c m ) and
( O C=14 m, ) find the area of the bed.
[Use ( left.pi=frac{22}{7}right] )
( A cdot 161.4 m^{2} )
в. ( 192.5 m^{2} )
c. ( 212.6 m^{2} )
D. ( 257.2 .5 m^{2} )
10
220The area of a segment of a circle of
radius ( 21 mathrm{cm} ) if the arc of the segment
has a measure of ( 60^{circ} ) is
(Take ( sqrt{mathbf{3}}=mathbf{1 . 7 3} ) )
A. 45.27 sq. ( mathrm{cm} )
B. 40.27 sq. ( mathrm{cm} )
c. 40.8 sq. ( mathrm{cm} )
D. none of these
10
22168. At the centres of two circles, two
arcs of equal length subtend an-
gles of 60° and 75° respectively.
The ratio of the radii of the two
circles is
(1) 5:2 (2) 5:4
(3) 3:2 (4) 2:1
10
222buckel
54. If the radii of the circular en
of a truncated conical bus
which is 45cm high be 28
and 7 cm, then the capacity
the bucket in cubic centimet
is user = 2
(1) 48510
(3) 48150
(2) 45810
(4) 48051
bant :
10
223Find the area of the shaded region in
fig., if ( boldsymbol{P} boldsymbol{Q}=mathbf{2 4 c m}, boldsymbol{P R}=mathbf{7 c m} ) and ( boldsymbol{O} ) is
the centre of the circle.
10
224Find the radius of a circle whose
circumference is ( 39.6 mathrm{cm} )
10
225In the figure. ( A C=24 mathrm{cm}, B C=10 )
and ( O ) is the
centre of the circle. Find the area of
shaded region
10
2261
70. In the figure, OED and OBA are
sectors of a circle with centre O.
The area of the shaded portion
is
4m
45°
-3m-
(1) m
2 6 m
m2
m2
10
227In a circle with center ( 0, ) central angle ( A O B ) has a measure of ( frac{5 pi}{4} ) radians. The area of the sector formed by central
angle ( A O B ) is what fraction of the area
of the circle?
A ( cdot frac{5}{8} )
B. ( frac{8}{5} )
c. ( frac{16}{5} )
D. ( frac{4}{5} )
10
228The area of a circle is ( 24.64 . m^{2} ) What is
the circumference of the circle?
A . ( 14.64 m )
B. 16.36 m
c. ( 17.60 m )
D. ( 18.40 m )
10
229In the given figure, the area of the
shaded portion APB is?
A ( -frac{1}{4} pi r^{2} )
B. ( frac{1}{4}(pi-2) r^{2} )
c. ( frac{1}{4}(pi-1) r^{2} )
D. None of these
10
23063.
A circle is inscribed in a square
of side 35 cm. The area of the
remaining portion of the square
which is not enclosed by the cir-
cle is
(1) 262.5 cm2 (2) 562.5 cm?
(3) 962.5 cm2 (4) 762.5 cm
10
231Consider a circle with unit radius. There
are seven adjacent sectors, ( S_{1}, S_{2}, S_{3} ldots S_{7}, ) in the circle such that
their total area is ( frac{1}{8} ) of the area of the circle. Further, the area of the jth sector
is twice that of the ( (j-1)^{t h} ) sector, for
( j=2, dots .7 )
Find the area of the sector ( boldsymbol{S}_{1} )
( mathbf{A} cdot frac{3 pi}{1016} )
В. ( frac{pi}{508} )
c. ( frac{pi}{1016} )
D. ( frac{pi}{336} )
10
232Given ( : A B=12 mathrm{cm}, A C=13 mathrm{cm}, mathrm{ED}=mathrm{FG}= )
( 5 mathrm{cm}, mathrm{EF}=10 mathrm{cm} ) and ( mathrm{GD}=4 mathrm{cm} )
Find the area and the perimeter of the
adjoining figure
( A cdot 88 ) sq. ( mathrm{cm} ) and ( 50 mathrm{cm} )
B. 88 sq. ( m ) and 50 cm
( c .88 ) sq. ( mathrm{cm} ) and ( 50 mathrm{m} )
D. 8.8 sq. ( mathrm{cm} ) and ( 50 mathrm{cm} )
10
23355. A metal wire when bent in the
form of a square encloses an area
484 cm. If the same wire is ben
in the form of a circle, then (tak
ing r = 22 ) its area is
(1) 308 cm2 (2) 506 cm
(3) 600 cm2 (4) 616 cm
10
234In the figure above, ( overline{A C} ) is a diameter of
the large circle and ( mathrm{B} ) lies on ( overline{boldsymbol{A C}} ) so that
( A B ) is a diameter of the small circle. If
( A B=1 ) and ( B C=2, ) Calculate the
area of the shaded region.
( A cdot frac{pi}{4} )
в.
( c cdot 2 pi )
D. ( frac{9 pi}{4} )
E . ( 9 pi )
10
235In the given figure find the value of
( angle A O C )
( mathbf{A} cdot 130^{circ} )
B. ( 140^{circ} )
( mathbf{c} cdot 150^{circ} )
D. ( 160^{circ} )
10
236If the radius of the circle is increased by
( 100 % ) then the area is increased by
A. ( 100 % )
B . 200%
c. 300%
D. 400%
10
237The circumference of a circular garden
is ( 572 m . ) Outside the garden a road,
( 3.5 m ) wide, runs around it.Calculate the
( operatorname{cost} ) of repairing the road at the rate of Rs.375per 100.sq.m?
10
238The area of a square of side 1610
239A design is made on a rectangular tile
of dimensions ( 50 mathrm{cm} 70 mathrm{cm} ) as shown in
Fig. ( 12.7 . ) The design shows 8 triangles,
each of sides ( 26 mathrm{cm}, 17 mathrm{cm} ) and ( 25 mathrm{cm} ) os
cut out. Find the total area of the design
in ( c m^{2} )
10
240If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:
A . 2 units
B. ( pi ) units
c. 4 units
D. 7 units
10
241If the ratio of circumference of two
circles is ( 4: 9, ) then what is the ratio of
their areas is?
A .9: 4
B. 16: 81
c. 4: 9
D. 2: 3
10
242A circular pond is of diameter ( 17.5 mathrm{m} ). It is surrounded by a ( 2 mathrm{m} ) wide path. Find the cost of constructing the path at the
rate of Rs. 25 per square metre (Use ( pi= )
3.14)
10
243A square has the perimeter ( 40 mathrm{cm} ) What is the sum of the diagonals?10
244The perimeter of a sector of a circle of
radius ( 5.7 m ) is ( 27.2 m . ) Find the area of
the sector.
10
245If the area of a triangle with base ( x ) is
equal to area of a square of side ( x, ) then the altitude of the triangle is
A ( cdot frac{x}{2} )
B. ( x )
( c cdot sqrt{2} x )
D. ( 2 x )
10
246When a circle is cut into eighths, those
sectors are called as,
A. Sextants
B. Quadrants
c. octants
D. None of these
10
247A wire is bent in the form of a square of
side ( 16.5 mathrm{cm} . ) It is straightened and then bent into a circle. What is the
radius of the circle so formed? ( left(text { Taken } pi=frac{22}{7}right) )
10
248A circular flower bed is surmounted by
a path ( 5 mathrm{m} ) wide as shown in fig.The
diameter of the flowerbed is ( 60 mathrm{m} ). What
is the area of this path?
( mathbf{A} cdot 735 pi c m^{2} )
В. ( 325 pi c m^{2} )
( mathbf{c} cdot 635 pi c m^{2} )
D. None of these
10
249In the figure, an equilateral triangle of side ( 6 mathrm{cm} ) and its circumcircle is shown
Find the area of shaded portion. Take ( (boldsymbol{pi}=mathbf{3 . 1 4}, sqrt{mathbf{3}}=mathbf{1 . 7 3}) )
A. ( 22.11 mathrm{cm}^{2} )
B. ( 22 mathrm{cm}^{2} )
c. ( 21.11 mathrm{cm}^{2} )
D. ( 23.11 mathrm{cm}^{2} )
10
250In the given figure, ( A C ) is diameter of ( a )
circle with radius ( 5 mathrm{cm} ). if ( mathrm{AB}=mathrm{BC} ) and
( mathrm{CD}=8 mathrm{cm}, ) the area of the shaded region
to the nearest whole number is-
( A cdot 28 c m^{2} )
B ( cdot 29 c m^{2} )
( c cdot 30 c m^{2} )
( mathbf{D} cdot 45 mathrm{cm}^{2} )
10
251The perimeter of a rectangular sheet is ( 100 mathrm{cm} . ) If the length is ( 35 mathrm{cm}, ) find its breath Also find the area.10
252Area of region bounded by ( boldsymbol{x}=mathbf{0}, boldsymbol{y}=mathbf{0} )
( boldsymbol{x}=mathbf{2}, boldsymbol{y}=mathbf{2}, boldsymbol{y} leq boldsymbol{e}^{x} ; boldsymbol{y} geq ln boldsymbol{x} ) is
A ( .6-4 ln 2 )
B. ( 4 ln 2-2 )
c. ( 2 ln 2-4 )
D. ( 6-2 ln 2 )
10
253In the figure, ( m ) ? ( P O Q=30 ) ? and radius ( O P )
( =12 mathrm{cm}, ) then find the given area of segment PRQ (Given ( pi=3.14) )
A ( cdot 1.68 c m^{2} )
B ( cdot 2 cdot 46 c m^{2} )
( c cdot 0.68 c m^{2} )
D. none of these
10
254A circle is inscribed in a square. If the
area of the square is 36 sq. units, what is the area of the circle?
( mathbf{A} cdot 6 pi )
в. ( 9 pi )
c. ( 12 pi )
D. ( 18 pi )
( E .36 pi )
10
255In the above figure, ( boldsymbol{O} ) is the centre of
the circle and ( angle B A C=n^{circ}, angle O C B= )
( m^{circ} ) then
A ( cdot m^{circ}+n^{circ}=90^{circ} )
B . ( m^{circ}+n^{circ}=180^{circ} )
( mathbf{c} cdot m^{circ}+n^{circ}=120 )
D . ( m^{circ}+n^{circ}=150^{circ} )
10
256f ( a r e a=900 s q . c m ) and breadth ( = )
( 25 mathrm{cm}, ) then find length of rectangle.
10
257( n )
Fig., ( A B C ) is a quadrant of a circle of radius ( 14 mathrm{cm} ) and a semicircle is drawn
with ( B C ) as diameter. Find the area of
the shaded region
10
258In a circle of radius ( 21 mathrm{cm}, ) an arc
subtends and angle of ( 60^{circ} ) at the centre.
Find:
(i) The length of the arc
(ii) Area of the
sector formed by the arc (iii) Area of the segment formed by the corresponding chord
10
259The length of a minute hand of a wall
clock is ( 8.4 mathrm{cm} . ) Find the area swept by it in half an hour.
A ( cdot 100 mathrm{cm}^{2} )
В. ( 110.88 mathrm{cm}^{2} )
( mathrm{c} cdot 120 mathrm{cm}^{2} )
D. ( 130 mathrm{cm}^{2} )
10

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