Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 638 · 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 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
2. 2.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 180 cu cm (b) 17 cu cm (c) 18 cu cm (d) 144 cu cm
3. 3.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 729 sq cm (d) 486 sq cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
5. 5.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
7. 7.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
8. 8.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
9. 9.A cuboid is 12 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 324 cu cm (b) 23 cu cm (c) 360 cu cm (d) 72 cu cm
10. 10.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq 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) 16 times (b) 4 times (c) 64 times (d) 8 times
14. 14.A cuboid is 9 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 450 cu cm (b) 72 cu cm (c) 648 cu cm (d) 26 cu cm
15. 15.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
16. 16.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) 9 times (c) 6 times (d) 27 times
17. 17.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
18. 18.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 14 cu cm (c) 84 cu cm (d) 122 cu cm
19. 19.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
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
21. 21.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
23. 23.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 15 cu cm (d) 136 cu cm
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
25. 25.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 80 sq cm (b) 264 sq cm (c) 132 sq cm (d) 66 sq cm
26. 26.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 168 cu cm (b) 188 cu cm (c) 17 cu cm (d) 24 cu cm
27. 27.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 97 sq cm (d) 96 sq cm
28. 28.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 726 cu cm
29. 29.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
30. 30.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) 8 times (c) 4 times (d) 5 times
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
33. 33.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 512 cu cm (d) 384 cu cm
34. 34.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
35. 35.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 144 cu cm (d) 18 cu cm
36. 36.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 368 sq cm (b) 120 sq cm (c) 184 sq cm (d) 92 sq cm
37. 37.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 126 sq cm (b) 162 sq cm (c) 324 sq cm (d) 81 sq cm
38. 38.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
39. 39.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
40. 40.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) 5 times (c) 125 times (d) 25 times

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