Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 451 · 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 cuboid is 6 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 12 cu cm (b) 17 cu cm (c) 168 cu cm (d) 108 cu cm
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
7. 7.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) 4 times (c) 2 times (d) 5 times
8. 8.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 66 sq cm (b) 72 sq cm (c) 264 sq cm (d) 132 sq cm
9. 9.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
10. 10.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) 27 times (c) 3 times (d) 9 times
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
12. 12.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
13. 13.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) 125 times (c) 25 times (d) 5 times
14. 14.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 576 sq cm (d) 144 sq cm
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
16. 16.A cuboid is 7 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 272 sq cm (b) 68 sq cm (c) 136 sq cm (d) 84 sq cm
17. 17.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 486 sq cm (d) 324 sq cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
20. 20.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 36 cu cm (d) 54 cu cm
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
23. 23.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 36 sq cm (d) 54 sq cm
24. 24.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) 5 times (c) 8 times (d) 4 times
25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 96 sq cm (d) 64 sq cm
26. 26.A cuboid is 10 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 752 sq cm (b) 480 sq cm (c) 188 sq cm (d) 376 sq cm
27. 27.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
29. 29.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 136 cu cm (b) 84 cu cm (c) 12 cu cm (d) 15 cu cm
30. 30.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 486 cu cm (d) 324 cu cm
31. 31.A cuboid is 8 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 320 cu cm (b) 40 cu cm (c) 288 cu cm (d) 21 cu cm
32. 32.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
35. 35.A cuboid is 12 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 432 cu cm (b) 48 cu cm (c) 384 cu cm (d) 25 cu cm
36. 36.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
37. 37.A cuboid is 11 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 208 sq cm (b) 176 sq cm (c) 104 sq cm (d) 416 sq cm
38. 38.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 65 cu cm (d) 96 cu cm
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
40. 40.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 294 sq cm (d) 343 sq cm

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