Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 882 · 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 the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
3. 3.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) 6 times (d) 27 times
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.A cuboid is 12 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 21 cu cm (b) 256 cu cm (c) 60 cu cm (d) 240 cu cm
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq 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) 3 times (b) 6 times (c) 27 times (d) 9 times
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
10. 10.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) 8 times (c) 6 times (d) 4 times
11. 11.A cuboid is 11 cm long, 9 cm wide and 6 cm high. What is its total surface area? (a) 219 sq cm (b) 438 sq cm (c) 876 sq cm (d) 594 sq cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
13. 13.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
14. 14.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
15. 15.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 576 cu cm (d) 1728 cu cm
16. 16.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 13 cu cm (b) 6 cu cm (c) 48 cu cm (d) 92 cu cm
17. 17.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
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
19. 19.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
20. 20.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 94 cu cm (b) 15 cu cm (c) 60 cu cm (d) 12 cu cm
21. 21.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
22. 22.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
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
24. 24.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
25. 25.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 90 cu cm (b) 126 cu cm (c) 15 cu cm (d) 14 cu cm
26. 26.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
27. 27.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 122 sq cm (b) 61 sq cm (c) 244 sq cm (d) 84 sq cm
28. 28.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
29. 29.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 144 sq cm (d) 1728 sq cm
30. 30.A cuboid is 11 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 88 cu cm (b) 880 cu cm (c) 29 cu cm (d) 556 cu cm
31. 31.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) 25 times (c) 10 times (d) 125 times
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
33. 33.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
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
35. 35.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
36. 36.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) 8 times (d) 4 times
37. 37.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) 64 times (d) 4 times
38. 38.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
39. 39.A cuboid is 9 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 22 cu cm (b) 72 cu cm (c) 360 cu cm (d) 314 cu cm
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times

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