Area questions ask how much surface a shape covers, or what it costs to cover or fence it.
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Q1. A circular ring is formed by two concentric circles of radii 98 cm and 84 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: C
Let outer radius = R = 98 cm and inner radius = r = 84 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 98^2 = 9604. r^2 = 84^2 = 7056. R^2 – r^2 = 9604 – 7056 = 2548. Area = (22/7) x 2548 = 8008 sq cm.
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Q2. A circular ring is formed by two concentric circles of radii 98 cm and 42 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: B
Let outer radius = R = 98 cm and inner radius = r = 42 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 98^2 = 9604. r^2 = 42^2 = 1764. R^2 – r^2 = 9604 – 1764 = 7840. Area = (22/7) x 7840 = 24640 sq cm.
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Q3. A circular ring is formed by two concentric circles of radii 112 cm and 77 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: D
Let outer radius = R = 112 cm and inner radius = r = 77 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 112^2 = 12544. r^2 = 77^2 = 5929. R^2 – r^2 = 12544 – 5929 = 6615. Area = (22/7) x 6615 = 20790 sq cm.
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Q4. A circular ring is formed by two concentric circles of radii 42 cm and 14 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: B
Let outer radius = R = 42 cm and inner radius = r = 14 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 42^2 = 1764. r^2 = 14^2 = 196. R^2 – r^2 = 1764 – 196 = 1568. Area = (22/7) x 1568 = 4928 sq cm.
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Q5. A circular ring is formed by two concentric circles of radii 133 cm and 84 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: A
Let outer radius = R = 133 cm and inner radius = r = 84 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 133^2 = 17689. r^2 = 84^2 = 7056. R^2 – r^2 = 17689 – 7056 = 10633. Area = (22/7) x 10633 = 33418 sq cm.
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Q6. A circular ring is formed by two concentric circles of radii 70 cm and 14 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: C
Let outer radius = R = 70 cm and inner radius = r = 14 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 70^2 = 4900. r^2 = 14^2 = 196. R^2 – r^2 = 4900 – 196 = 4704. Area = (22/7) x 4704 = 14784 sq cm.
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Q7. A circular ring is formed by two concentric circles of radii 14 cm and 7 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: D
Let outer radius = R = 14 cm and inner radius = r = 7 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 14^2 = 196. r^2 = 7^2 = 49. R^2 – r^2 = 196 – 49 = 147. Area = (22/7) x 147 = 462 sq cm.
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Q8. A circular ring is formed by two concentric circles of radii 70 cm and 35 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: B
Let outer radius = R = 70 cm and inner radius = r = 35 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 70^2 = 4900. r^2 = 35^2 = 1225. R^2 – r^2 = 4900 – 1225 = 3675. Area = (22/7) x 3675 = 11550 sq cm.
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Q9. A circular ring is formed by two concentric circles of radii 91 cm and 63 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: A
Let outer radius = R = 91 cm and inner radius = r = 63 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 91^2 = 8281. r^2 = 63^2 = 3969. R^2 – r^2 = 8281 – 3969 = 4312. Area = (22/7) x 4312 = 13552 sq cm.
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Q10. A circular ring is formed by two concentric circles of radii 140 cm and 84 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: D
Let outer radius = R = 140 cm and inner radius = r = 84 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 140^2 = 19600. r^2 = 84^2 = 7056. R^2 – r^2 = 19600 – 7056 = 12544. Area = (22/7) x 12544 = 39424 sq cm.
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Q11. A circular ring is formed by two concentric circles of radii 35 cm and 21 cm. Find the area of the ring. (Take pi = 22/7)
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Answer: C
Let outer radius = R = 35 cm and inner radius = r = 21 cm, with pi = 22/7. The ring’s area is the outer circle’s area minus the inner circle’s area, not (R – r)^2. So area = pi x R^2 – pi x r^2 = pi x (R^2 – r^2). R^2 = 35^2 = 1225. r^2 = 21^2 = 441. R^2 – r^2 = 1225 – 441 = 784. Area = (22/7) x 784 = 2464 sq cm.
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Q12. Find the area of a semicircle with radius 42 cm. (Take pi = 22/7)
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Answer: B
Let radius = R = 42 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 42^2 = 5544 sq cm. A semicircle is exactly half of that. Area = 5544 / 2 = 2772 sq cm.
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Q13. Find the area of a semicircle with radius 154 cm. (Take pi = 22/7)
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Answer: C
Let radius = R = 154 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 154^2 = 74536 sq cm. A semicircle is exactly half of that. Area = 74536 / 2 = 37268 sq cm.
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Q14. Find the area of a semicircle with radius 56 cm. (Take pi = 22/7)
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Answer: D
Let radius = R = 56 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 56^2 = 9856 sq cm. A semicircle is exactly half of that. Area = 9856 / 2 = 4928 sq cm.
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Q15. Find the area of a semicircle with radius 196 cm. (Take pi = 22/7)
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Answer: A
Let radius = R = 196 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 196^2 = 120736 sq cm. A semicircle is exactly half of that. Area = 120736 / 2 = 60368 sq cm.
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Q16. Find the area of a semicircle with radius 98 cm. (Take pi = 22/7)
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Answer: D
Let radius = R = 98 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 98^2 = 30184 sq cm. A semicircle is exactly half of that. Area = 30184 / 2 = 15092 sq cm.
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Q17. Find the area of a semicircle with radius 126 cm. (Take pi = 22/7)
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Answer: C
Let radius = R = 126 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 126^2 = 49896 sq cm. A semicircle is exactly half of that. Area = 49896 / 2 = 24948 sq cm.
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Q18. Find the area of a semicircle with radius 168 cm. (Take pi = 22/7)
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Answer: B
Let radius = R = 168 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 168^2 = 88704 sq cm. A semicircle is exactly half of that. Area = 88704 / 2 = 44352 sq cm.
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Q19. Find the area of a semicircle with radius 84 cm. (Take pi = 22/7)
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Answer: A
Let radius = R = 84 cm, and take pi = 22/7. A full circle of this radius has area pi x R^2 = (22/7) x 84^2 = 22176 sq cm. A semicircle is exactly half of that. Area = 22176 / 2 = 11088 sq cm.
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Q20. Find the circumference of a circle with radius 42 cm. (Take pi = 22/7)
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Answer: D
Let radius = R = 42 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 42 = 264 cm.
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Q21. Find the circumference of a circle with radius 168 cm. (Take pi = 22/7)
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Answer: A
Let radius = R = 168 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 168 = 1056 cm.
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Q22. Find the circumference of a circle with radius 70 cm. (Take pi = 22/7)
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Answer: C
Let radius = R = 70 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 70 = 440 cm.
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Q23. Find the circumference of a circle with radius 140 cm. (Take pi = 22/7)
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Answer: B
Let radius = R = 140 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 140 = 880 cm.
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Q24. Find the circumference of a circle with radius 98 cm. (Take pi = 22/7)
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Answer: B
Let radius = R = 98 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 98 = 616 cm.
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Q25. Find the circumference of a circle with radius 49 cm. (Take pi = 22/7)
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Answer: A
Let radius = R = 49 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 49 = 308 cm.
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