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Class 10 Maths Chapter 12 Area Related to Circles

1.If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then

(a) R1 + R2 = R

(b) R1² + R2² = R²

(c) R1 + R2 < R

(d) R1² + R2² < R²

Answer: (b) R12 + R22 = R2

2. The perimeter of a circle having radius 5cm is equal to:

(a)30 cm

(b)3.14 cm

(c)31.4 cm

(d)40 cm

Answer: (c)31.4 cm

3. Perimeter of a sector of a circle whose central angle is 90° and radius 7 cm is

(a) 35 cm

(b) 25 cm

(c) 77 cm

(d) 7 cm

Answer: (b) 25 cm

4. The area of the circle is 154 cm2. The radius of the circle is

(a) 7 cm

(b) 14 cm

(c) 3.5 cm

d) 17.5 cm

Answer:(a) 7 cm

5. If angle of sector is 60°, radius is 3.5 cm then length of the arc is

(a) 3 cm

(b) 3.5 cm

(c) 3.66 cm

(d) 3.8 cm

Answer: (c) 3.66 cm

6. The area of a circle whose circumference is 22 cm, is

(a) 11 cm²

(b) 38.5 cm²

(c) 22 cm²

(d) 77 cm²

Answer:(b) 38.5 cm²

7. A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

(a) 15.8 km/hr

(b) 16.2 km/hr

(c) 11 km/hr

(d) 18 km/hr

Answer: (a) 15.8 km/hr

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8. If the circumference of a circle and the perimeter of a square are equal, then

(a) Area of the circle = Area of the square

(b) Area of the circle > Area of the square

(c) Area of the circle < Area of the square

(d) Nothing definite can be said about the relation between the areas of the circle and square.

Answer: (b) Area of the circle > Area of the square

9. Area of the circle with radius 5cm is equal to:

(a)60 sq.cm

(b)75.5 sq.cm

(c)78.5 sq.cm

(d)10.5 sq.cm

Answer: (c)78.5 sq.cm

10. The area of a circle that can be inscribed in a square of side 10 cm is

(a) 40π cm²

(b) 30π cm²

(c) 100π cm²

(d) 25π cm²

Answer: (d) 25π cm²

11. horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 7 m long rope. The area of that part of the field in which the horse can graze, is

(a) 77 cm²

(b) 77/2 cm²

(c) 154 cm²

(d) 77/4 cm²

Answer: (b) 77/2 cm²

12. The area of the circle whose diameter is 21 cm is

(a) 346.5 cm²

(b) 37.68 cm²

(c) 18.84 cm²

(d) 19.84 cm²

Answer: (a) 346.5 cm²

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13. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has circumference equal to the sum of the circumference of two circles is

(a) 35 cm

(b) 10 cm

(c) 21 cm

(d) 28 cm

Answer: (d) 28 cm

14. A car has wheels which are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minute when the car is travelling at a speed of 66km per hour?

(a) 5000

(b) 4375

(c) 5400

(d) 4400

Answer: (b) 4375

15. Area of the largest triangle that can be inscribed in a semi-circle of radius r units, in square units is:

(a) r²

(b) 1/2r²

(c) 2 r²

(d) √2r²

Answer: (a) r²

16. If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to:

(a)14:11

(b)22:7

(c)7:22

(c)11:14

Answer: (a)14:11

17. The perimeter of a square circumscribing a circle of radius a units is

(a) 2 units

(b) 4α units

(c) 8α units

(d) 16α units

Answer: (c) 8α units

18. The area of the sector of a circle with radius 6 cm and of angle 60° is

(a) 9.42 cm²

(b) 37.68 cm²

(c) 18.84 cm²

(d) 19.84 cm²

Answer: (c) 18.84 cm²

19. The area of a circle whose circumference is 22 cm, is

(a) 11 cm²

(b) 38.5 cm²

(c) 22 cm²

(d) 77 cm²

Answer: (b) 38.5 cm²

20. The area of a sector of a circle bounded by an arc of length 5π cm is equal to 20π cm2, then its radius is

(a) 12 cm

(b) 16 cm

(c) 8 cm

(d) 10 cm

Answer: (c) 8 cm

21. The cost of fencing a circular field at the rate Rs24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m². Find the cost of ploughing the field.(Take Π=22/7)

(a) Rs 2000

(b) Rs 1900

(c) Rs 1925

(d) Rs 1800

Answer: (c) Rs 1925

22. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be

(a) 10 m

(b) 15 m

(c) 20 m

(d) 24 m

Answer: (a) 10 m

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23. The area of the circle that can be inscribed in a square of side 8 cm is

(a)36 π cm²

(b)16 π cm²

(c)12 π cm²

(d)9 π cm²

Answer: (b)16 π cm²

24.The perimeter of the sector with radius 10.5 cm and sector angle 60° is

(a) 32 cm

(b) 23 cm

(c) 41 cm

(d) 11 cm

Answer: (a) 32 cm

25. The area of a circle whose circumference is 22 cm, is

(a) 11 cm²

(b) 38.5 cm²

(c) 22 cm²

(d) 77 cm²

Answer: (b) 38.5 cm²

26. The area of a circle is 154 cm². Its diameter is

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

Answer: (b) 14 cm

27. The radii of two circles are 4 cm and 3 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

Answer: (c) 10

28. The side of a square is 10cm. The area of circumscribed and inscribed circles.?

(a) 157 cm², 78.5cm²

(b) 150 cm², 75cm²

(c) 147 cm², 78.5cm²

(d) 157 cm², 79.5cm²

Answer: (a) 157 cm², 78.5cm²

29. The area of the circle that can be inscribed in a square of side 6 cm is

(a) 36 π cm²

(b) 18 π cm²

(c) 12 π cm²

(d) 9 π cm²

Answer:  (d) 9 π cm2

30. The area of the square that can be inscribed in a circle of radius 8 cm is

(a)256 cm2

(b)128 cm2

(c)642 cm2

(d)64 cm2

Answer: (b)128 cm2

31. In a circle of diameter 42 cm, if an arc subtends an angle of 60° at the centre, where π = 227 then length of arc is

(a) 11 cm

(b) 22/7 cm

(c) 22 cm

(d) 44 cmAnswer

Answer: (c) 22 cm

32. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is

(a) 153.9 cm²

(b) 102.6 cm²

(c) 51.3 cm²

(d) 205.2 cm²

Answer: (c) 51.3 cm²

33. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has circumference equal to the sum of the circumference of two circles is

(a) 35 cm

(b) 10 cm

(c) 21 cm

(d) 28 cm

Answer: (d) 28 cm

34. If the area of a circle is 154 cm², then its perimeter is

(a) 11cm

(b) 22 cm

(c) 44 cm

(d) 55 cm

Answer: (c) 44 cm

35. The sum of the radii of two circles is 140cm and the difference of their circumference is 88cm.Find the diameters of the circles.

(a) 150 cm, 88 cm

(b) 158 cm,122 cm

(c) 160 cm,120 cm

(d) 154cm, 126 cm

Answer: (d) 154cm, 126 cm

36. The area of the square that can be inscribed in a circle of radius 8 cm is

(a) 256 cm²

(b) 128 cm²

(c) 642 cm²

(d) 64 cm²

Answer:  (B)

37. The area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.

(a)142/7

(b)152/7

(c)132/7

(d)122/7

Answer: (c)132/7

38. The perimeter of a sector of radius 5.2 cm is 16.4 cm, the area of the sector is

(a) 31.2 cm²

(b) 15 cm²

(c) 15.6 cm²

(d) 16.6 cm²

Answer: (c) 15.6 cm²

39. The radii of two circles are 4 cm and 3 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is [Delhi 2011]

(a) 5

(b) 7

(c) 10

(d) 14

Answer: (c) 10

40. The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

(a) 8 a

(b) 4 a

(c) 2 a

(d) 16

Answer: (a) 8 a

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41. If θ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is

(a) πr2^θ/360

(b)  πr2^θ/180

(c)  πrθ/180

(d)  πrθ/90

Answer: (a) πr2^θ/360

42. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is

(a) 56 cm

(b) 42 cm

(c) 28 cm

(d) 16 cm

Answer: (c) 28 cm

43. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is;

(a)20cm

(b)21cm

(c)22cm

(d)25cm

Answer: (c)22cm

44. If the radius of a circle is doubled, its area becomes

(a) 2 times

(b) 4 times

(c) 8 times

(d) 16 times

Answer: (b) 4 times

45. If the area of a circle is numerically equal to twice its circumference, then the diameter of the circle is

(a) 4 units

(b) n units

(c) 8 units

(d) 2 units

Answer: (c) 8 units

46. The ratio of area of two circles whose ratio of circumference is 3:1 will be

(a) 3 : 1

(b) 1 : 3

(c) 1 : 9

(d) 9 : 1

Answer: (d) 9 : 1

47. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles?

(a) 9 cm

(b) 10 cm

(c) 15 cm

(d) 11 cm

Answer: (b) 10 cm

48. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm respectively, is

(a) 31 cm

(b) 25 cm

(c) 62 cm

(d) 50 cm

Answer: (d) 50 cm

49. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is:

(a)200 cm²

(b)220 cm²

(c)231 cm²

(d)250 cm²

Answer: (c)231 cm²

50. The perimeter of a circular and square fields are equal. If the area of the square field is 484 m² then the diameter of the circular field is

(a) 14 m

(b) 21 m

(c) 28 m

(d) 7 m

Answer: (c) 28 m

51. If the circumference of a circle is 352 metres, then its area in square metres is

(a) 5986

(b) 6589

(c) 7952

(d) 9856

Answer: (d) 9856

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52. The area of the square that can be inscribed in a circle of radius 12 cm is

(a) 288 sq. cm

(b) 576 sq. cm

(c) 144 sq.cm

(d) 500 sq. cm

Answer: (a) 288 sq. cm

53. Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm

(a) 44 cm

(b) 88 cm

(c) 22 cm

(d) 66 cm

Answer: (b) 88 cm

54. If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then

(a) the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.

(b) the angle of the corresponding sector of the first circle is equal the angle of the corresponding sector of the other circle.

(c) the angle of the corresponding sector of the first circle is half the angle of the corresponding sector of the other circle.

(d) the angle of the corresponding sector of the first circle is 4 times the angle of the corresponding sector of the other circle.

Answer: (a) the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.

55. Area of a sector of angle p (in degrees) of a circle with radius R is

(a)p/180 × 2πR

(b)p/180 × π R²

(c)p/360 × 2πR

(d)p/720 × 2πR²

Answer: (d)p/720 × 2πR²

56. The radius of sphere is r cm. It is divided into . two equal parts. The whole surface area of two parts will be

(a) 8πr² cm²

(b) 6πr² cm²

(c) 4πr² cm²

(d) 3πr² cm²

Answer: (b) 6πr² cm²

57. The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is

(a) 2670 m

(b) 2880 m

(c) 1980 m

(d) 1596 m

Answer: (c) 1980 m

58. The ratio of the areas of the incircle and circumcircle of a square is

(a) 1 : 2

(b) 1 : 3

(c) 1 : 4

(d) 1 : √2

Answer: (a) 1 : 2

59. If a square is inscribed in a circle, find the ratio of the areas of the circle and the square?

(a) π:2

(b) 2:π

(c) π:4

(d) 4:π

Answer: (a) π:2

60. The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h?

(a) 300

(b) 400

(c) 450

(d) 500

Answer: (d) 500

61. If the diameter of a semicircular protractor is 14 cm, then its perimeter is .

(a) 27 cm

(b) 36 cm

(c) 18 cm

(d) 9 cm

Answer: (b) 36 cm

62. Area of the largest triangle that can be inscribed in a semi-circle of radius r units is [NCERT Exemplar Problems]

(a) r² sq. units

(b) 1/2 r² sq. units

(c) 2 r² sq. units

(d) 2/ r² sq. units

Answer: (a) r² sq. units

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63. The distance covered by a circular wheel of diameter ‘d’ in 100 revolutions is

(a) 100π

(b) 100d

(c) πd

(d) 100πd

Answer: (d) 100πd

64. Which one of these is True

(a) Distance travelled by a circular wheel of diameter z cm in one revolution is 2πz2πz cm

(b) The area of the circle inscribed in a square of side x cm, πx²cm²πx²cm²

(c) If the area of a circle is 154 cm² , then its perimeter is 55 cm

(d) The perimeter of a square circumscribing a circle of radius y cm is 8y cm

Answer: (d) The perimeter of a square circumscribing a circle of radius y cm is 8y cm

65. A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20m × 16m, then the area of the field in which the cow can graze is:

(a) 154 m²

(b) 156 m²

(c) 158 m²

(d) 160 m²

Answer:(a) 154 m²

66. A race track is in the form of a circular ring whose outer and inner circumferences are 396 m and 352 m respectively. The width of the track is

(a) 63 m

(b) 56 m

(c) 7 m

(d) 3.5 m

Answer: (c) 7 m

67. If the difference between the and the radius of of a circle is 37 cm, then 22 using π=227 the circumference (in cm) of the circle is:

(a) 154

(b) 44

(c) 14

(d) 7

Answer: (b) 44

68. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be

(a) 10 m

(b) 15 m

(c) 20 m

(d) 24 m

Answer: (a) 10 m

69. A car travels 1km distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.

(a) 35.35 cm

(b) 34.35 cm

(c) 35.50 cm

(d) None of these

Answer:(a) 35.35 cm

70. Area of a sector of central angle 120° of a circle is 3π cm2. Then the length of the corresponding arc of this sector is:

(a) 5.8cm

(b) 6.1cm

(c) 6.3cm

(d) 6.8cm

Answer: (c) 6.3cm

71. The area of the largest triangle that can be inscribed in a semicircle of radius r is

(a) r²

(b) 2r²

(c) r³

(d) 2r³

Answer: (a) r²

72. If 7i is taken as 227, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is

(a) 2.2

(b) 1.1

(c) 9.625

(d) 96.25

Answer: (b) 1.1

73. The area of the circle that can be inscribed in a square of side 10cm is

(a) 25 sq.cm

(b) 10π sq.cm

(c) 125π sq.cm

(d) 20π sq.cm

Answer: (c) 125π sq.cm

74. Two circles touch externally. The sum of their areas is 58 cm² and the distance between their centres is 10 cm. Find the radii of the two circles

(a) 6 cm, 4 cm

(b) 7cm, 3cm

(c) 9 cm , 1 cm

(d) 8 cm ,2 cm

Answer: (b) 7cm, 3cm

75. A round table cover has six equal designs . If the radius of thecover is 28 cm, then the cost of making the design at the rate of Rs. 0.35 per cm² is:

(a) Rs.146.50

(b) Rs.148.75

(c) Rs.152.25

(d) Rs.154.75

Answer: (b) Rs.148.75

76. The area (in cm²) of the circle that can be inscribed in a square of side 8 cm is

(a) 64 π

(b) 16 π

(c) 8 π

(d) 32 π

Answer: (b) 16 π

77. If the circumferences of two circles are in the ratio 4: 9, then the ratio in their area is

(a) 9: 4

(b) 4: 9

(c) 2: 3

(d) 16: 81

Answer: (d) 16: 81

78. If ‘r’ is the radius of a circle, then its perimeter is given b

y(a) πr

(b) 2πr

(c) 2πd

(d) none of these

Answer: (b) 2πr

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79. The diameter of a circle whose area is equal to sum of the areas of the two circles of radii 40 cm and 9 cm is

(a) 41 cm

(b) 49 cm

(c) 82 cm

(d) 62 cmAnswer

Answer: (c) 82 cm

80. The ratio of the areas of the incircle and circumcircle of a square is

(a) 1: 2

(b) 1: 3

(c) 1: 4

(d) 1: 6

Answer: (a) 1: 2

81. The area of a circle is 2464 sq. cm, then its diameter is given by

(a) 7cm

(b) 14cm

(c) 28cm

(d) 56cm

Answer: (d) 56cm

82. A circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6: 5. The smaller side of the rectangle is

(a) 30 cm

(b) 60 cm

(c) 70 cm

(d) 80 cm

Answer: (b) 60 cm

83. The perimeter of a semicircular protractor whose radius is 7cm is

(a) 18cm

(b) 27cm

(c) 36cm

(d) 72cm

Answer: (c) 36cm

84. The circumference of a circle exceeds its diameter by 120cm, then its radius is

(a) 56cm

(b) 14cm

(c) 42cm

(d) 28cm

Answer: (d) 28cm

85. If the radius of a circle is increased by 100%, then its area is increased by

(a) 100%

(b) 300%

(c) 200%

(d) 400%

Answer: (b) 300%

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