Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 632 · 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.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
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
5. 5.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
6. 6.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) 25 times (c) 10 times (d) 5 times
7. 7.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
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
9. 9.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
10. 10.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
11. 11.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
12. 12.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 217 cu cm (d) 216 cu cm
13. 13.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 56 sq cm (b) 112 sq cm (c) 224 sq cm (d) 64 sq cm
14. 14.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) 2 times (c) 5 times (d) 4 times
15. 15.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 108 cu cm (b) 552 cu cm (c) 864 cu cm (d) 29 cu cm
16. 16.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
17. 17.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) 64 times (c) 4 times (d) 16 times
18. 18.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 36 sq cm (d) 9 sq cm
19. 19.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 84 cu cm (b) 12 cu cm (c) 15 cu cm (d) 136 cu cm
20. 20.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
21. 21.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
22. 22.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 188 cu cm (b) 42 cu cm (c) 168 cu cm (d) 17 cu cm
23. 23.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
24. 24.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
25. 25.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 121 sq cm (d) 726 sq cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
27. 27.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
28. 28.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 33 cu cm (d) 1331 cu cm
29. 29.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
30. 30.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
31. 31.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 17 cu cm (b) 168 cu cm (c) 24 cu cm (d) 188 cu cm
32. 32.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 18 sq cm (c) 42 sq cm (d) 84 sq cm
33. 33.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
34. 34.A cuboid is 7 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 188 cu cm (b) 28 cu cm (c) 17 cu cm (d) 168 cu cm
35. 35.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
36. 36.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
37. 37.A cuboid is 11 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 117 sq cm (b) 198 sq cm (c) 234 sq cm (d) 468 sq cm
38. 38.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
40. 40.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

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