Sheet MENSURATION – 2D

07
– 2D
12. The diameter of a cycle wheel is 126 cm. A cyclist
1 (a) 12325 (b) 18750
takes 16 minutes to reach the destination at a (c) 21000 (d) 24350
2
speed of 72 km/hr. How many revolution will the 16. The cost of leveling a circular field at 50 Paisa per
wheel make during the journey?/ square meter is Rs.7700. The cost (in Rs) of put-
ting up a fence all round it at Rs.1.20 per meter is

1
2

(a) 5000 (b) 5200  xy 

Useπ 
(c) 4500 (d) 4000  n 
13. A gear 12 cm in diameter is turning a gear 18 cm (a) Rs.132 (b) Rs.264
in diameter. When the smaller gear has 42 revo- (c) Rs.528 (d) Rs. 1056
lutions. how many has the larger one made?
17. A person observed that he required 30 seconds
less time to cross a circular ground along its di-
ameter than to cover it once along the boundary.
If his speed was 30 m/minutes. then the radius of
(a) 28 (b) 20 
 xy 

the circular ground is Useπ
(c) 15 (d) 24  n 
14. The diameter of the front wheel of an engine is 2x
cm and that of rear wheel is 2y cm. to cover the
same distance, find the number of times the rear
wheel will revolve when the front wheel revolves
‘n’ times.
(a) 5.5 m (b) 7.5 m
x (c) 10.5 m (d) 3.5 m
y 18. In the given figure, PQR is a quadrant whose ra-
n dius is 7 cm. A circle is inscribed in the quadrant
as shown in the figure. What is the area (in cm2 of
the circle?
n yn PQR
(a) xy times (b) times
x
²
nx xy
(c) y times (d) times (a) 385–221 2 (b) 308–154 2
n
15. Diameter of wheel of a cycle is 21 cm, the cyclist (c) 154–77 2 (d) 402–308 2
takes 45 minutes to reach a destination at a speed
of 16.5 km per hr How many revolutions will the
wheel make during the journey?

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 21. The area of the circle with radius Y is W. The dif-
ference between the areas of the bigger circle (ra-
dius with radius Y) and that of the smaller circle

x
(with radius X) is W’. So
y is equal to:/ Y

W Y

x
X W
y

w' w'
(a) 1– (b) 1+
w w

w w
19. Four semi circles of equal radius are drawn on the (c) 1+ (d) 1–
w' w'
diameter of a semi circle having radius 56. Find
the radius of the bigger circle inscribed in the semi 1. If the angle of the sector is 90° and the radius is 6
circle as given below./ cm, then the area of the sector is .
90°

(a) 22 (b) 112 (c) 22.4 (d) 28 (a) 24 cm2 (b) 9π cm 2

20. As shown in the given figure, inside the larger semi- (c) 9 cm2 (d) 36 cm2
circle, three semicircles (having equal radius) are 2. If the diameter of a circle is 14 cm, find the area of
drawn so that the diameter of all of them sit on the sector of the circle whose central angle is 60°./
the diameter of the larger semicircle. What is the 14 cm
ratio between the white and yellow areas?
(a) 38.12 cm2 (b) 25.66 cm2
(c) 21.66 cm 2
(d) 18.12 cm2
3. An arc on a circle that is 15 cm long subtended a
24° angle at the center. What is the circmference
of the circle ?/ 24°
(a) 4 : 3 (b) 2 : 1
(c) 1 : 2 (d) 3 : 4
(a) 240 cm (b) 220 cm
(c) 236 cm (d) 225 cm
4. The sector is cut from a circle of diameter 42 cm.
If the angle of the sector is 150°, then its area (in
cm2) is–/
150°

(a) 564 (b) 574

(c) 850.6 (d) 577.5
5. What is the length of the arc of a circle whose
radius is 35 cm and arc subtends an angle of 36°
 22 
π =
at the centre of the circle?  
 7 

36°

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 A is equal to./60°
 22 
π =
 
 A C A
 7 
(a) 44 cm (b) 22 cm c2 c2 c2 c2
(a) (b) (c) (d)
(c) 10 cm (d) 220 cm 6π 18π 24π 4π
6. The perimeter of a sector of a circle is 24 cm and 14. The perimeter of a minor sector of a circle of ra-
radius is 3 cm. Find the area (in cm2) of the sec- dius 5 cm is 15.5 cm. Find the area of the minor
tor./
 22 
Use it : π =
sector  
 /5 cm
(a) 24 (b) 27 (c) 33 (d) 30  7 
7. The perimeter of a sector of a circle of radius 6 cm 15.5 cm
is 25 cm. What is the area of the sector ?/  22 
π = 
 7 
(a) 38 cm2 (b) 54 cm2 (a) 17.53 cm2 (b) 13.75 cm2
(c) 39 cm2 (d) 56 cm2 (c) 13.57 cm2 (d) 17.35 cm2
8. The perimeter of a sector of a circle of radius 5.2
cm is 16.4 cm. What is the area of the sector ?/ 15. Find the perimeter of the major sector of a circle
of radius 12 m, whose minor sector subtends an
angle of 75° at the center./

(a) 15.6 sq.cm (b) 15 sq.cm

75°
(c) 14.4 sq. cm (d) 14.1 sq. cm
9. The perimeter of a sector of a circle of radius 7.4 (a) 2 4 – 4 π m (b) 24 + 5 π m
cm is 20.6 cm. The area of this sector is:
(c) 2 4 + 1 9 π m (d) 2 4 – 1 9 π m
7.4 cm 20.6 cm
16. The minute hand of a clock is 20 cm long. Find
the area on the face of the clock swept by the
(a) 42.92 cm2 (b) 5.8 cm2 minute hand between 8 a.m. and 8 : 45 a.m.
(c) 10.73 cm2 (d) 21.46 cm2
20 cm 8 a.m.
10. An arc of length 23.1 cm subtends an 18° angle
8 : 45 a.m
at the center. What is the area of the circle?/23.1
18°
 22  6600 6600
(a) cm2 (b) cm2
Use : π =  7 9
 7 
(a) 16988.50 cm2 (b) 16878.50 cm2 6600 6600
(c) cm2 (d) cm2
(c) 16898.50 cm2 (d) 16978.50 cm2 18 14
11. The arc length of a sector of a circle that sub- 17. AB and CD are respectively arcs of two concentric
tends a 22.5° angle at the center is given as 16.5 circles of radii 21 cm and 7 cm and centre O. If
cm. What will be the radius (in cm) of the circle?
 AOB = 30°, find the area of the shaded region.
22.5°
AB CD O
16.5 cm
 AOB = 30°
(a) 35 (b) 49 (c) 42 (d) 48
(a) 102.67 cm2 (b) 203.76 cm2
12. The area of the sector of a circle is 128 cm2. If the
length of the arc of that sector is 64 cm, then find (c) 305.87 cm2 (d) 353.57 cm2
the radius of the circle. 18. In the figure, OED and OBA are sectors of a circle
with centre O. The area of the shaded portion. /
128 cm2
OED OBA
O
(a) 16 cm (b) 4 cm (c) 8 cm (d) 2 cm
13. The area of a sector of a circle with central angle
60° is A. The circumference of the circle is C. Then

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 11 2 11 2  22 
(a) m (b) m  Take : π =
 

16 8  7 
11 2 11 2 (a) 70 m (b) 75 m
(c) m (d) m (c) 80 m (d) 65 m
2 4
21. The sides of a triangle are 10 cm, 24 cm and 26
cm. At each of its vertices, circle of radius 3.5 cm
are drawn. What is the area of the triangle ex-
cluding the portion covered by the sectors of the
circle ?

3.5

 22 
π = 
 7 
(a) 100.75 cm2 (b) 81.5 cm2
(c) 75.75 cm2 (d) 78.25 cm2
19. The following diagram shows part of a fan. OAD
and OFG are sectors of a circle with center O,
having radius 24cm. The central angle of the sec-
tors is 45° as shown in the figure. B, C, H and E
lie on a circle with center O and radius 8 cm. What
is the shaded area (in cm²) Take π = 3.14
OAD OFG O
24 cm
45° B, C, H
E O 8 cm (cm )? ( π = 3.14
2
)
(a) 425.16 (b) 452.16
(c) 620.88 (d) 602.88

22. At each corner of a triangular field of sides 20 m,

34 m and 42 m. A horse is tied by a rope of 7 m.
Find the area of ungrazed field by the horses ?

(a) 259 m2 (b) 277 m2

(c) 231 m2 (d) 247 m2
20. A horse is tied to a post by a rope. If the horse
moves along a circular path always keeping the
rope stretched and describes 88 meters when it
has traced out 72° at the centre, the length of the
rope is.

72°

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23. The sides of a triangle are 24 cm, 26 cm and 10
cm. A circle of radius 4.2 cm is drawn centred at
each of its vertices. Find the area (in cm2) of the
triangle, except for the part covered by the seg-
ments of the circle.

4.2

(a) 105.86 (b) 27.71 (c) 92.8 (d) 120

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