CIRCUMFERENCE AND AREA OF A CIRCLE
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1 CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given figure, find the area of the unshaded portion within the rectangle. (Take = 3.14) 3. In an equilateral triangle ABC of side 14 cm, side BC is the diameter of a semi-circle as shown in the figure. Find the area of the (Take = 22 and 7 3 = 1.732) ASSIGNMENT AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of the shaded portion in 308 cm 2, calculate : (i) the length of AC, and (ii) the circumference of the F 22I circle. Take K J 7 HG 9. PS is a diameter of a circle of radius 6 cm. Q and R are points on the diameter such that PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the figure. Find the perimeter of the [ = 3.14] 10. In the given figure, the area enclosed between the two concentric circles is 770 cm 2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle. 11. Calculate the area of the The quadrants shown in the figure are each of radius 7 cm. 4. In the given figure, AB is the diameter of a circle with centre O and OA = 7 cm. Find the area of the 5. A rectangular playground has two semicircles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m and 21 m, find the area of the playground. ( = 22/7) [Take 22 7 ] 12. The figure shows a running track surrounding a grassed enclosure PQRSTU. The enclosure consists of rectangle PQST with a semi-circular region at each end. PQ = 200 m and PT = 70 m. 6. In the given figure, OACB is a quadrant of a circle. The radius OA = 3.5 cm., OD = 2 cm. Calculate the area of the shaded portion. 7. A sheet is 11 cm long and 2 cm wide. Circular pieces 0.5 cm in diameter are cut from it to prepare discs. Calculate the number of discs that can be prepared. 1 (i) Calculate the area of the grassed enclosure in m 2. (ii) Given that the track is of constant width 7 m, calculate the outer perimeter ABCDEF of the track. (Take to be 22 7 )
2 13. The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/ h. Give your answer correct to the nearest km. 14. A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed for 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket. 22 [Take 7 ] ANSWERS cm 2, cm cm cm cm m cm (i) 28 cm (ii) 88 cm cm cm cm (i) m 2 (ii) 664 m km/h
3 1. A garden is in the circular shape whose area is 9856 m 2. Calculate the cost of fencing the garden at Rs 5 per metre. 2. Find the radius of a circle whose circumference is equal to the sum of the circumferences of three circles whose radii are 1 cm, 2 cm and 3 cm. 3. What is the area of a circle, the circumference of which is equal to the perimeter of the square of side 11 cm? 4. A wire is in the form of a circle of radius 35 cm. It is bent in the form of a square. Find the area of the square. 5. Find the circumference of the circle whose area is 16 times the area of the circle with diameter 1.4 m. 6. The circumference of a circle exceeds its diameter by 180 cm. Calculate the (i) radius (ii) circumference and (iii) area of the circle. 7. Wire forming an equilateral triangle of side 22 cm is bent to form a circle. Calculate : (i) radius of the circle formed (ii) area of the circle. 8. The perimeter of a semi-circle is 32.4 cm. Calculate : (i) the radius of the circle (ii) the area of the circle. 9. The perimeter of the quadrant of a circle is 100 m. Find the area of the circle. 10. The area of a ring is 264 cm 2. If the radius of the smaller circle is 4 cm, find the radius of the bigger circle. 11. The areas of two concentric circles are cm 2 and 1386 cm 2 respectively. Find the width of the ring. 12. The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the radii of the two circles. 13. The sum of the radii of two circles is 84 cm and the difference of their areas is 5544 cm 2. Calculate the radii of the two circles. 14. Two circles touch internally. If the distance between their centres is 4 cm and sum of their areas is 170 cm 2, find the radii of the circles. 15. Prove that the area of a circular path of uniform width k surrounding a circular region of radius r is k (k + 2r). 16. The inner circumference of a circular race track is 352 m. The track is everywhere 2.5 m wide. Calculate the cost of : (i) levelling the track at the rate of Rs 1.80 per m 2. (ii) putting up a fence along the outer circle at the rate of Rs 3.25 per metre. 17. A cart is driven at 7 km/hour. If each wheel is 70 cm in diameter, find the number of revolutions made by each wheel per minute. 18. Wheel of a car makes 4 revolutions per second. If the diameter of the wheel is 84 cm, find the speed of the car. ASSIGNMENT Two circles touch externally. The sum of their areas is 130 cm 2 and the distance between their centres is 14 cm. Determine the radii of the circles. 20. A boy draws the largest possible circle on a piece of square paper. The circumference of the circle is 220 cm. Find : (i) the side of the square. (ii) the area of the circle. 21. The length of a rectangle is twice its breadth. Semi-circles are drawn on the lengths as shown. Given that the perimeter of the figure is 58 cm, calculate : (i) the dimensions of the rectangle. (ii) the area of the figure. 22. In an equilateral triangle of side 24 cm, a circle is inscribed, touching its sides. Find the area of the remaining portion of the triangle. ( and 314. ). 23. In the figure, a circle is inscribed in a square of side 14 cm. Calculate : (i) the area of the circle. (ii) the area of the shaded portion. 24. In the figure, B is the midpoint of AC and AC = 28 cm. Three semi-circles are drawn as AC, AB and BC as diameters. Calculate the area and perimeter of the shaded portion. 25. In the figure, square OABC is drawn in the sector DOE. If the radius of the sector ABC is 20 cm, find the area of the shaded portion. (Use = 3.14) 26. Four equal circles each of radius 4.5 cm touch each other as shown in the figure. Find the area of the 3
4 27. In the figure, OAB is a quadrant of a circle of radius 7 cm bounded by perpendicular lines OA and OB. If OP = 4 cm and OQ = 3 cm, calculate : (i) the area of the shaded portion. (ii) the perimeter of the shaded portion. 28. In the figure, ABCD is a square of side 10 cm. Calculate the area of the shaded portion. 29. The diagram represents the area swept by the wiper of a car. With the dimensions, given in the diagram, calculate the shaded area swept by the wiper. 30. In the figure, XYZ is an equilateral triangle inscribed in a circle of radius 4 cm with centre O. Find the area of the 31. In the figure, four corners are circle quadrants and a circle is in the middle of the square. Find the perimeter and area of the (Take = 3.142) 32. Find the area of the shaded region in the figure. 33. The figure shows a gate of a house. The height and breadth of each rectangular pillar are 3 m and 14 cm respectively. The top arch is bounded by two concentric circles. If the gate has uniform width throughout and the width of the entrance is 2.1 m, calculate : (i) the maximum height of the gate. (ii) the area of the face of the gate. 34. In the figure, PQ = 216 cm and R is the mid-point of PQ. Semicircles are drawn on PQ, PR and RQ as diameters. A circle with centre S is drawn which touches all the three semi-circles. Find : (i) the radius of the circle with S as centre. (ii) the area of the 35. In the figure, two circles with centres A and B touch each other at the point T. If AT = 14 cm, and AB = 3.5 cm, find the area of the 36. In the figure, ABC is an equilateral triangle of side 14 cm. If O is the centre of the circumcircle, find the area of the shaded region. 37. In the figure, BCD is a quadrant of a circle of radius 21 cm and ABCD is a square. CEF is an isosceles triangle whose equal sides are 4 cm. Find the area of the shaded region. 38. In the figure, ABCD is a trapezium in which AB DC and ABC = 90. Four sectors are removed with A, B, C, D as centres and radius of each sector = 3.5 cm. If BC = CD = 14 cm, and AB = 21 cm, find the area of the shaded portion. ANSWERS 1. Rs cm cm cm m 6. (i) 42 cm (ii) 264 cm (iii) 5544 cm 2 7. (i) 10.5 cm (ii) cm 2 8. (i) 6.3 cm (ii) cm cm cm cm cm, 63 cm cm, 31.5 cm cm, 7 cm 16. (i) Rs (ii) Rs m/sec cm, 3 cm 20. (i) 70 cm (ii) 3850 cm (i) 7 cm, 14 cm (ii) 252 cm 2 4
5 cm (i) 154 cm 2 (ii) 42 cm cm 2, 88 cm cm cm (i) 32.5 cm 2 (ii) 23 cm cm cm e j cm cm, 9.71 cm cm (i) 4.05 m (ii) cm (i) 36 cm (ii) 1620 cm cm cm cm cm 2. 5
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