Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 715 · 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.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
3. 3.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) 9 times (c) 27 times (d) 3 times
4. 4.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) 64 times (d) 16 times
5. 5.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) 4 times (c) 8 times (d) 16 times
6. 6.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 81 sq cm (d) 324 sq cm
7. 7.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) 4 times (c) 16 times (d) 64 times
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
10. 10.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
12. 12.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
13. 13.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
15. 15.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
17. 17.A cuboid is 8 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 584 sq cm (b) 336 sq cm (c) 292 sq cm (d) 146 sq cm
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq 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) 9 times (c) 6 times (d) 27 times
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
21. 21.A cuboid is 11 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 44 sq cm (c) 96 sq cm (d) 192 sq cm
22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
23. 23.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 864 cu cm (d) 1728 cu cm
24. 24.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 9 sq cm (d) 27 sq cm
25. 25.A cuboid is 12 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 27 cu cm (b) 84 cu cm (c) 472 cu cm (d) 672 cu cm
26. 26.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
27. 27.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) 4 times (c) 8 times (d) 6 times
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
30. 30.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
31. 31.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
32. 32.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 48 cu cm (b) 49 cu cm (c) 12 cu cm (d) 88 cu cm
33. 33.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 97 sq cm (c) 16 sq cm (d) 64 sq cm
34. 34.A cuboid is 8 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 92 sq cm (b) 184 sq cm (c) 160 sq cm (d) 368 sq cm
35. 35.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 8 cu cm (c) 17 cu cm (d) 16 cu cm
36. 36.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) 6 times (c) 27 times (d) 9 times
37. 37.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 144 sq cm
38. 38.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 17 cu cm (b) 120 cu cm (c) 30 cu cm (d) 164 cu cm
39. 39.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 126 sq cm (b) 380 sq cm (c) 95 sq cm (d) 190 sq cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 64 sq cm (b) 32 sq cm (c) 16 sq cm (d) 12 sq cm

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