Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 525 · 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) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
2. 2.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
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 area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
5. 5.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
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
7. 7.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
8. 8.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
9. 9.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
10. 10.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
11. 11.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 54 cu cm (d) 9 cu cm
12. 12.A cuboid is 7 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 121 sq cm (b) 242 sq cm (c) 484 sq cm (d) 210 sq cm
13. 13.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 42 sq cm (b) 18 sq cm (c) 21 sq cm (d) 84 sq cm
14. 14.A cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 105 cu cm (b) 142 cu cm (c) 15 cu cm (d) 106 cu cm
15. 15.A cuboid is 8 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 528 sq cm (b) 132 sq cm (c) 264 sq cm (d) 288 sq cm
16. 16.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 1196 sq cm (b) 990 sq cm (c) 598 sq cm (d) 299 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
19. 19.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
20. 20.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 576 sq cm (d) 144 sq cm
21. 21.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
22. 22.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 144 sq cm (d) 36 sq cm
23. 23.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 72 cu cm (c) 17 cu cm (d) 132 cu cm
24. 24.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 24 sq cm (d) 16 sq cm
25. 25.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
26. 26.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
27. 27.A cuboid is 7 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 210 sq cm (b) 214 sq cm (c) 428 sq cm (d) 107 sq 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.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
30. 30.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
31. 31.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 40 sq cm (b) 38 sq cm (c) 76 sq cm (d) 152 sq cm
32. 32.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
33. 33.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 108 sq cm (b) 324 sq cm (c) 81 sq cm (d) 162 sq cm
34. 34.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
35. 35.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) 16 times (c) 4 times (d) 64 times
36. 36.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
37. 37.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 100 sq cm
38. 38.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 174 sq cm (b) 135 sq cm (c) 87 sq cm (d) 348 sq cm
40. 40.A cuboid is 12 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 144 sq cm (b) 96 sq cm (c) 384 sq cm (d) 192 sq cm

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