1. In fig., ABC is a right triangle right angled at A. Find thearea of shaded region if AB = 6 cm, BC = 10 cm and O isthe centre of the incircle of ABC. (Take = 3.14)

2. The area of an equilateral triangle is cm2. Takingeach angular point as centre, circles are drawn withradius equal to half the length of the side of the triangle.Find the area of triangle not included in the circles.

(Take = 1.73)3. In fig. AOBPA is quadrant of a circle of radius 14 cm. A

semicircle with AB as diameter is drawn. Find the area ofthe shaded region.

4. Four circles are described about the four corners of asquare so that each touches two of the others as shownin fig. Find the area of the shaded region, each side ofthe square is 14 cm. (Take = 22/7)

5. In the fig., find the perimeter of shaded region whereADC, AEB and BFC are semicircles on diameters AC, ABand BC respectively.

ORFind the area of the shaded region in the fig., whereABCD is a square of side 14 cm.

6. In fig., ABC is a right-angled triangle, right-angled at A.Semicircles are drawn on AB, AC and BC as diameters.Find the area of the shaded region.

7. In the fig., ABC is a quadrant of a circle of radius 14 cmand a semi-circle is drawn with BC as diameter. Find thearea of the shaded region.

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8. In fig., PQ = 24 cm, PR = 7 cm and O is the centre of thecircle. Find the area of shaded region. (Take = 3.14)

9. In figure, the shape of the top of a table in a restaurantis that of a sector of a circle with centre O andBOD = 900. If BO = OD = 60 cm, find.(i) the area of the top of the table (ii) Theperimeter of the table top. (Take = 3.14)

OR

In fig., ABCD is a square of side 14 cm and APD and BPCare semicircles. Find the area of shaded region.

(Take = 22/7)10. In fig., AB and CD are two perpendicular diameters of a

circle with centre O. If OA = m7 cm. find the area of theshaded region. (Take = 22/7)

11. In the fig. O is the centre of a circle. The area of sector

OAPB is of the area of the circle. Find x.

12. In fig., if ATO = 400, find AOB.

13. Find the perimeter of the given figure, where AED is asemi circle and ABCD is a rectangle.

14. If the diameter of a semicircular protractor is 14 cm,then find it’s perimeter.

15. The length of the minute hand of a wall clock is 7 cm.How much area does it sweep in 20 minutes?

16. A sheet is 11 cm long and 2 cm wide. Circular pieces 0.5cm in diameter are cut from it to prepare discs.Calculate the number of discs that can be prepared

17. Find the circumference and area of a circle of radius17.5 cm.

18. Find the circumference and area of a circle of diameter91 cm.

19. Find the circumference and area of a circle of radius 15

cm. (Take20. The circumference of a circle is 123.2 cm. Taking

calculate:(i) the radius of the circle in cm;(ii) the area of the circle in cm2, correct to the nearestcm(iii) the effect on the area of the circle if the radius isdoubled

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21. Find the length of a rope by which a cow must betethered in order that it may be able to graze an area of9856 m2.

22. The area of a circle is 394.24 cm2. Calculate :(i)The radius of the circle, (ii) The circumference of thecircle.

23. Find the perimeter and area of a semi-circular of a plate

of radius 25 cm (Take24. The perimeter of a semi-circular metallic plate is 86.4

cm. Calculate the radius and area of the plate.25. The circumference of a circle exceeds its diameter by

180 cm. Calculate(i) The radius (ii) The circumference and

(iii) The area of the circle.26. A copper wire when bent in the form of a square

encloses an area of 272.25 cm2. If the same wire is bentinto the form of a circle, what will be the area enclosedby the wire?

27. A copper wire when bent in the form of a equilateral

triangle has an area of 121 cm2. If the same wire isbent into the form of a circle, find the area enclosed bythe wire.

28. The circumference of a circle field is 528 m.29. The cost of levelling a circular field at Rs2 per sq. metre

is Rs 33957. Calculate:(i) The area of the field; (ii) The radius of then field;

(iii) The circumference of the field;(iv) The cost of fencing it at Rs 2.75 per metre.

30. The cost of fencing a circular field at Rs 9.50 per metre isRs 2926. Find the cost of ploughing the field at Rs 1.50per sq. metre.

31. AC and BD are two perpendicular diameters of a circleABCD. Given that the area of the shaded portion is 308cm2, calculate : (i) The length of AC; and (ii) Thecircumference of the circle.

32. The sum of the radii of two circles is 140 cm and thedifference of their circumferences is 88 cm. Find theradii of the two circles.

33. The sum of the radii of two circles is 84 cm and thedifference of their areas is 5544 cm2. Calculate the radiiof the two circles .

34. Two circles touch externally. The sum of their areas is117 cm2 and the distance between their centres is 15cm. Find the radii of the two circles.

35. Two circles touch internally. The sum of their areas isand the distance between then centres is 4 cm. Find theradii of the circles.

36. Find the area of a ring whose outer and inner radii are19 cm and 16 cm respectively.

37. A path of width 8 m runs around a circular park whoseradius is 38 m. Find the area of the path.

38. The areas of two concentric circles are 962.5 cm2 and1386 cm2 respectively. Find the width of the ring.

39. The area enclosed between two concentric circles is 770cm2. If the radius of the outer circle is 21 cm, calculatethe radius of the inner circle.

40. In the given figure, the area enclosed between twoconcentric circles is 808.5 cm2. The circumference of theouter circle is 242 cm. Calculate : (i) the radius of theinner circle, (ii) the width of the ring.

41. Find the area of a circle circumscribing an equilateraltriangle of side 15 cm. [Take = 3.14].

42. Find the area of a circle inscribed in an equilateraltriangle of side 18 cm. [Take = 3.14].

43. The shape of the top of a table in a restaurant is that ofa segment of a circle with centre O and BOD = 900.BO = OD = 60 cm. Find: (i) The area of the top of thetable; (ii) The perimeter of the table. [Take = 3.14].

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44. In the given figure, ABCD is a square of side 5 cminscribed in a circle. Find:(i) The radius of the circle, (ii) The area of the shadedregion. [Take = 3.14]

45. In the given figure, ABCD is a rectangle inscribed in acircle. If two adjacent sides of the rectangle be 8 cm and6 cm, calculate : (i) The radius of the circle; and (ii) Thearea of the shaded region. [Take = 3.14].

46. In the given figure, ABCD is a piece of cardboard in theshape of a trapezium in which AB || DC, ABC = 900.From this piece, quarter circle BEFC is removed. GivenDC = BC = 4.2 cm and AE = 2 cm.Calculate the area of the remaining piece of thecardboard.

47. Find the perimeter and area of the shaded region in thegiven figure. (Take = 3.142).

48. In the given figure, PQRS is a diameter of a circle ofradius 6 cm. The lengths PQ, QR and RS are equal.Semi-circles are drawn on PQ and QS as diameters. If PS= 12 cm, find the perimeter and the area of the shadedregion. [Take = 3.14].

49. Find the perimeter and area of the shaded region shownin the figure. The four corners are circle quadrants andat the centre, there is a circle. [Take = 3.14].

50. In the given figure, find the area of the unshadedportion within portion within the rectangle. [Take =3.14].

51. In the given figure, ABCP is a quadrant of circle of radius14 cm. With AC as diameter, a semi-circle is drawn. Findthe area of the shaded region.

52. In the given, OACB is a quadrant of a circle. The radiusOA = 3.5 cm, OD = 2 cm. Calculate the area of theshaded portion.

53. In the given figure, ABCD is a square of side 14 cm and A,B, C, D are centres of circular arcs, each of radius 7 cm.Find the area of the shaded region.

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54. In the given figure, two circles with centres A and Btouch each other at the point T. If AT = 14 cm and AB =3.5 cm, find the area of the shaded region.

55. In the adjoining figure, the inside perimeter of a runningtrack with semi-circular ends and straight parallel sidesis 312 m. The length of the straight portion of the trackis 90 m. If the track has a uniform width of 2 mthroughout, find its area.

56. In the given figure, ABCD is a square of side 7 cm and A,B, C, D are centres of equal circles which touchexternally in pairs. Find the area of the shaded region.

57. In the given figure, AB is the diameter of a circle withcentre O and OA = 7 cm. Find the area of the shadedregion.

58. The diameter of a wheel is 1.26 m. How far will it travelin 500 revolutions?

59. The wheel of the engine of a train m incircumference makes 7 revolutions in 3 seconds. Findthe speed of the train in km per hour.

60. A toothed wheel of diameter 50 cm is attached to asmaller wheel of diameter 30 cm. How many revolutionswill the smaller wheel make when the larger one makes30 revolutions?

61. A wheel makes 1000 revolutions in covering a distanceof 88 km. Find the radius of the wheel.

62. A chord AB of a circle of radius 15 cm makes an angle of600 at the centre of the circle. Find the area of the major

and minor segment. (Take p = 3.14, = 1.73)63. In a circle of radius 21 cm, an arc subtends an angle of

600 at the centre. Find:(i) length of the ar(ii) area of the sector formed by the arc(iii) area of the segment formed by the correspondingchord of the arc.

64. A chord of a circle of radius 10 cm subtends a right angleat the centre. Find:(i) area of the minor sector (ii) area of theminor segment(iii) area of the major sector (iv) area of the majorsegment (Use p = 3.14)

65. Four equal circles are described about the four cornersof a square so that each touches two of the others asshown in Fig. Find the area of the shaded region, eachside of the square measuring 14 cm.

66. Find the areas of the shaded region in the Fig.

67. In an equilateral triangle of side 24 cm, a circle isinscribed touching its sides. Find the area of the

remaining portion of the triangle

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68. An athletic track 14 m wide consists of two straightsections 120 m long joining semi-circular ends whoseinner radius is 35 m. Calculate the area of the shadedregion.

69. The area of an equilateral triangle is cm2. Takingeach angular point as centre, a circle is described withradius equal to half the length of the side of the triangleas shown in Fig. Find the area of the triangle notincluded in the circle.

70. The area of an equilateral triangle is 1732.05 cm2. Abouteach angular point as centre, a circle is described withradius equal to half the length of the side of the triangle.Find the area of the triangle not included in the circles(Use p = 3.14)

71. A round table cover has six equal designs as shown inFig. If the radius of the cover is 28 cm, find the cost ofmaking the designs at the rate of Rs 3.50 per cm2. (Use

)

72. The area of a circle inscribed in an equilateral triangle is154 cm2. Find the perimeter of the triangle. [Use p =

22/7 and = 1.73]73. A park is in the form of a rectangle 120m × 100 m. At the

centre of the park there is a circular lawn. The area ofpark excluding lawn is 8700 m2. Find the radius of thecircular lawn. (Use p = 22/7)

74. The area of enclosed between the concentric circles is770 cm2. If the radius of the outer circle is 21 cm, findthe radius of the inner circle.

75. Find the circumference and area of a circle of radius 4.2cm.

76. Find the circumference of a circle whose area is 301.84cm2.

77. A steel wire when bent in the form of a square enclosesand area of 121 cm2. If the same wire is bent in theform of a circle, find the area of the circle.

78. A plot is in the form of a rectangle ABCD havingsemi-circle on BC as shown in Fig. If AB = 60 m and BC =28 m, find the area of the plot.

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79. Four equal circles, each of radius 5 cm, touch each otheras shown in Fig. Find the area included between them(Take p = 3.14).

80. Four cows are tethered at four corners of a square plotof side 50 m, so that they just cannot reach one another.What area will be left ungrazed ?

81. Calculate the circumference and area of a circle ofradius 5.6 cm.

82. The circumference of a circle is 123.2 cm. Calculate :(i) the radius of the circle in cm,(ii) the area of the circle, correct to nearest cm2

83. The area of a circle is 301.84 cm2. Calculate(i) the radius of the circle in cm.(ii) the circumference of the circle, correct to nearest

cm.m84. The perimeter of a semi-circular protractor is 32.4 cm.

Calculate :(i) the radius of the protractor in cm,(ii) the area of the protractor in cm2.

85. The area enclosed by the circumferences of twoconcentric circles is 346.5 cm2. If the circumference ofthe inner circle is 88 cm, calculate the radius of theouter circle.

86. Two circles touch externally. The sum of their areas is130 sq. cm and distance between their centres is 14cm. Determine the radii of the circles.

87. Two circles touch internally. The sum of their areas is116 sq. cm and the distance between their centres is6 cm. Find the radii of the given circles.

88. The wheel of a cart is making 5 revolutions per second.If the diameter of the wheel is 84 cm, find its speed inkm/hr. Give your answer, correct to nearest km.

89. The diameter of the driving wheel of a bus is 140 cm.How many revolutions must the wheel make in order tokeep a speed of 66 km/hr?

90. A bucket is raised from a well by means of a rope whichis wound round a wheel of diameter 77 cm. Given thatthe bucket ascends in 1 min. 28 seconds with a uniformspeed of 1.1 m / sec, calculate the number of completerevolutions the wheel makes in raising the bucket.

91. The figure shows a running track surrounding a grassenclosure PQRSTU. The enclosure consists of a rectanglePQST with a semi-circular region at each end. Given, PQ= 200 m and PT = 70 m.

(i) Calculate the area of the grassed enclosure in m2.(ii) Given that the track is of constant width 7 m,calculate the outer perimeter ABCDEF to the track.

92. In an equilateral triangle of side 24 cm, a circle isinscribed, touching its sides. Find the area of the

remaining portion of the triangle. Take = 1.73 and= 3.14.

93. In the given figure, a circle circumscribes a rectanglewith sides 12 cm and 9 cm. Calculate :(i) the circumference of the circle to nearest cm,(ii) the area of the shaded region, correct to 2 places ofdecimal, in cm2.Take = 3.14.

94. A chord of a circle of radius 14 cm makes a right angle atthe centre. Calculate :

95. The minute hand of a clock is 10.5 cm long. Find the areaswept by it in 15 minutes.

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