Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 814 · 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 9 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 63 cu cm (b) 382 cu cm (c) 504 cu cm (d) 24 cu cm
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
3. 3.A cuboid is 9 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 540 sq cm (b) 204 sq cm (c) 408 sq cm (d) 816 sq cm
4. 4.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 384 cu cm (d) 256 cu cm
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
7. 7.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 343 cu cm (d) 294 cu cm
8. 8.A cuboid is 7 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 105 sq cm (b) 284 sq cm (c) 71 sq cm (d) 142 sq cm
9. 9.A cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 142 sq cm (b) 105 sq cm (c) 71 sq cm (d) 284 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) 9 times (b) 3 times (c) 27 times (d) 6 times
11. 11.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 65 cu cm (d) 12 cu cm
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
13. 13.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
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
15. 15.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
16. 16.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) 3 times (c) 9 times (d) 27 times
17. 17.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
18. 18.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
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
21. 21.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) 5 times (c) 8 times (d) 2 times
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
25. 25.A cuboid is 6 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 256 sq cm (d) 128 sq cm
26. 26.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
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm
28. 28.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 600 cu cm
29. 29.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
31. 31.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
32. 32.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
33. 33.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
34. 34.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 320 sq cm (b) 96 sq cm (c) 80 sq cm (d) 160 sq cm
35. 35.If the side of a square 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
36. 36.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 729 cu cm (c) 324 cu cm (d) 27 cu cm
37. 37.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) 5 times (d) 125 times
38. 38.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 15 cu cm (d) 150 cu cm
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
40. 40.If the side of a square 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

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