Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 795 · 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 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 384 cu cm (d) 24 cu cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
3. 3.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 64 sq cm (c) 256 sq cm (d) 512 sq cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
6. 6.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
8. 8.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 112 sq cm (c) 56 sq cm (d) 28 sq cm
9. 9.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 54 sq cm (b) 204 sq cm (c) 102 sq cm (d) 51 sq cm
10. 10.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 16 cu cm (d) 8 cu cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
13. 13.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 64 cu cm (b) 10 cu cm (c) 8 cu cm (d) 32 cu cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
16. 16.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 17 cu cm (b) 174 cu cm (c) 135 cu cm (d) 15 cu cm
17. 17.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
18. 18.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
19. 19.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
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
21. 21.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
22. 22.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
23. 23.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
24. 24.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 200 sq cm (b) 440 sq cm (c) 220 sq cm (d) 110 sq cm
25. 25.A cuboid is 9 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 207 sq cm (b) 567 sq cm (c) 414 sq cm (d) 828 sq cm
26. 26.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 16 sq cm (d) 97 sq cm
27. 27.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 294 sq cm (c) 196 sq cm (d) 343 sq cm
28. 28.A cuboid is 12 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 792 sq cm (b) 504 sq cm (c) 198 sq cm (d) 396 sq cm
29. 29.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
30. 30.A cuboid is 8 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 480 sq cm (b) 376 sq cm (c) 752 sq cm (d) 188 sq cm
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
32. 32.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
33. 33.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
34. 34.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
35. 35.A cuboid is 12 cm long, 7 cm wide and 6 cm high. What is its volume? (a) 84 cu cm (b) 504 cu cm (c) 396 cu cm (d) 25 cu cm
36. 36.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
37. 37.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
38. 38.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 576 cu cm (d) 1728 cu cm
39. 39.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its total surface area? (a) 276 sq cm (b) 864 sq cm (c) 1104 sq cm (d) 552 sq cm
40. 40.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) 9 times (d) 27 times

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