Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 236 · 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.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 13 cu cm (b) 92 cu cm (c) 6 cu cm (d) 48 cu cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
6. 6.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) 8 times (c) 2 times (d) 4 times
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
8. 8.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) 3 times (d) 27 times
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 204 sq cm (b) 51 sq cm (c) 54 sq cm (d) 102 sq cm
11. 11.A cuboid is 9 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 540 sq cm (b) 816 sq cm (c) 408 sq cm (d) 204 sq cm
12. 12.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
14. 14.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
17. 17.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
18. 18.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 24 cu cm (b) 120 cu cm (c) 15 cu cm (d) 148 cu cm
19. 19.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
20. 20.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 6 times (d) 2 times
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
25. 25.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
27. 27.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
28. 28.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
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
30. 30.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
31. 31.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 384 sq cm (d) 64 sq cm
32. 32.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 280 cu cm (b) 300 cu cm (c) 30 cu cm (d) 21 cu cm
33. 33.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
34. 34.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 32 sq cm (b) 128 sq cm (c) 64 sq cm (d) 65 sq cm
35. 35.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 240 sq cm (b) 268 sq cm (c) 536 sq cm (d) 134 sq cm
36. 36.A cuboid is 11 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 132 sq cm (b) 100 sq cm (c) 400 sq cm (d) 200 sq cm
37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
38. 38.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 196 sq cm (c) 343 sq cm (d) 49 sq cm
39. 39.A cuboid is 12 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 240 cu cm (b) 60 cu cm (c) 256 cu cm (d) 21 cu cm
40. 40.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) 27 times (c) 6 times (d) 3 times

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