Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 618 · 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.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 484 cu cm
2. 2.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
5. 5.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 96 sq cm (d) 64 sq cm
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
7. 7.A cuboid is 12 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 29 cu cm (b) 84 cu cm (c) 548 cu cm (d) 840 cu cm
8. 8.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 576 cu cm (d) 1728 cu cm
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
11. 11.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 36 sq cm (b) 73 sq cm (c) 144 sq cm (d) 72 sq cm
12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
14. 14.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 9 sq cm (d) 36 sq cm
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
16. 16.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 729 sq cm (d) 486 sq cm
17. 17.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 8 times (d) 2 times
18. 18.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 180 sq cm (b) 360 sq cm (c) 90 sq cm (d) 144 sq cm
19. 19.A cuboid is 7 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 336 cu cm (b) 21 cu cm (c) 292 cu cm (d) 42 cu cm
20. 20.A cuboid is 11 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 26 cu cm (b) 77 cu cm (c) 442 cu cm (d) 616 cu cm
21. 21.A cuboid is 11 cm long, 9 cm wide and 5 cm high. What is its total surface area? (a) 796 sq cm (b) 495 sq cm (c) 398 sq cm (d) 199 sq cm
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
25. 25.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 172 cu cm (c) 112 cu cm (d) 56 cu cm
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
27. 27.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
28. 28.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
29. 29.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
31. 31.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 80 cu cm (c) 18 cu cm (d) 13 cu cm
32. 32.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 17 cu cm (b) 120 cu cm (c) 40 cu cm (d) 164 cu cm
33. 33.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
35. 35.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 188 cu cm (b) 24 cu cm (c) 168 cu cm (d) 17 cu cm
36. 36.A cuboid is 12 cm long, 9 cm wide and 7 cm high. What is its volume? (a) 756 cu cm (b) 510 cu cm (c) 28 cu cm (d) 108 cu cm
37. 37.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
38. 38.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm
39. 39.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
40. 40.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 8 sq cm (c) 4 sq cm (d) 16 sq cm

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