Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 56 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
3. 3.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 2 times (d) 6 times
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
5. 5.A cuboid is 11 cm long, 9 cm wide and 5 cm high. What is its total surface area? (a) 398 sq cm (b) 495 sq cm (c) 796 sq cm (d) 199 sq cm
6. 6.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
7. 7.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
10. 10.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
11. 11.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 21 cu cm (d) 294 cu cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
13. 13.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
14. 14.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
17. 17.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 343 sq cm (c) 196 sq cm (d) 49 sq cm
18. 18.A cuboid is 11 cm long, 9 cm wide and 6 cm high. What is its volume? (a) 594 cu cm (b) 26 cu cm (c) 99 cu cm (d) 438 cu cm
19. 19.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 384 sq cm (d) 64 sq cm
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
21. 21.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 42 sq cm (b) 18 sq cm (c) 21 sq cm (d) 84 sq cm
22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
24. 24.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 15 cu cm (b) 8 cu cm (c) 72 cu cm (d) 124 cu cm
25. 25.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 114 sq cm (b) 216 sq cm (c) 456 sq cm (d) 228 sq cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
27. 27.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 80 cu cm (c) 13 cu cm (d) 36 cu cm
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
29. 29.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its volume? (a) 598 cu cm (b) 30 cu cm (c) 99 cu cm (d) 990 cu cm
30. 30.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
31. 31.A cuboid is 11 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 17 cu cm (b) 99 cu cm (c) 33 cu cm (d) 150 cu cm
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
33. 33.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
35. 35.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
37. 37.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
38. 38.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
39. 39.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm

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