Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 320 · 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 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
2. 2.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) 16 times (c) 64 times (d) 8 times
3. 3.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
4. 4.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) 5 times (d) 125 times
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 600 sq cm
6. 6.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 76 sq cm (b) 304 sq cm (c) 96 sq cm (d) 152 sq 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.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
9. 9.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 384 cu cm (d) 512 cu cm
10. 10.A cuboid is 8 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 320 cu cm (b) 304 cu cm (c) 22 cu cm (d) 32 cu cm
11. 11.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
12. 12.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
14. 14.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
15. 15.A cuboid is 9 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 416 sq cm (b) 576 sq cm (c) 208 sq cm (d) 832 sq cm
16. 16.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
19. 19.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its volume? (a) 990 cu cm (b) 30 cu cm (c) 598 cu cm (d) 99 cu cm
20. 20.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 24 sq cm (c) 20 sq cm (d) 96 sq 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) 616 cm (d) 176 cm
22. 22.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
23. 23.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
25. 25.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
26. 26.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
27. 27.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 729 cu cm (d) 324 cu cm
28. 28.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) 16 times (c) 64 times (d) 4 times
29. 29.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 42 sq cm (b) 82 sq cm (c) 164 sq cm (d) 41 sq cm
30. 30.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 400 cu cm (c) 30 cu cm (d) 600 cu cm
31. 31.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 272 sq cm (b) 136 sq cm (c) 68 sq cm (d) 84 sq cm
32. 32.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 62 cu cm (b) 15 cu cm (c) 30 cu cm (d) 10 cu cm
33. 33.A cuboid is 10 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 276 cu cm (b) 21 cu cm (c) 280 cu cm (d) 40 cu cm
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
35. 35.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 12 cu cm (d) 64 cu cm
36. 36.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 212 sq cm (b) 424 sq cm (c) 106 sq cm (d) 144 sq cm
37. 37.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 24 cu cm (d) 16 cu cm
38. 38.A cuboid is 10 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 180 cu cm (b) 90 cu cm (c) 21 cu cm (d) 256 cu cm
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm

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