Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 863 · 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 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
3. 3.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) 27 times (d) 6 times
4. 4.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
5. 5.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 100 cu cm (d) 150 cu cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
7. 7.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
8. 8.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 39 sq cm (b) 156 sq cm (c) 45 sq cm (d) 78 sq cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
11. 11.A cuboid is 11 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 244 sq cm (b) 66 sq cm (c) 61 sq cm (d) 122 sq cm
12. 12.A cuboid is 10 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 30 cu cm (b) 320 cu cm (c) 23 cu cm (d) 300 cu cm
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
14. 14.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
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
17. 17.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
18. 18.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 18 cu cm (d) 216 cu cm
19. 19.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) 125 times (c) 10 times (d) 5 times
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
21. 21.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
22. 22.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
23. 23.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 512 sq cm (d) 64 sq cm
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
25. 25.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 864 sq cm (d) 144 sq cm
26. 26.A cuboid is 10 cm long, 8 cm wide and 8 cm high. What is its volume? (a) 80 cu cm (b) 640 cu cm (c) 26 cu cm (d) 448 cu cm
27. 27.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
29. 29.A cuboid is 10 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 160 sq cm (b) 116 sq cm (c) 464 sq cm (d) 232 sq cm
30. 30.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
31. 31.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) 4 times (c) 2 times (d) 8 times
32. 32.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 400 cu cm (c) 600 cu cm (d) 30 cu cm
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
34. 34.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 16 sq cm (d) 24 sq cm
35. 35.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
36. 36.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) 27 times (d) 9 times
37. 37.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) 4 times (d) 2 times
38. 38.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 9 cu cm (d) 52 cu cm

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