Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 816 · 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 radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
2. 2.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) 10 times (c) 25 times (d) 125 times
3. 3.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) 4 times (c) 16 times (d) 8 times
4. 4.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
5. 5.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) 5 times (c) 10 times (d) 25 times
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
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) 27 times (b) 9 times (c) 3 times (d) 6 times
9. 9.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
13. 13.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 40 cu cm (c) 76 cu cm (d) 11 cu cm
14. 14.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 42 sq cm (c) 18 sq cm (d) 84 sq cm
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
18. 18.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) 25 times (d) 125 times
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
20. 20.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 45 sq cm (b) 54 sq cm (c) 90 sq cm (d) 180 sq cm
21. 21.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
22. 22.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
23. 23.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
24. 24.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 396 cu cm (b) 24 cu cm (c) 99 cu cm (d) 358 cu cm
25. 25.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
26. 26.A cuboid is 8 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 24 cu cm (b) 48 cu cm (c) 480 cu cm (d) 376 cu cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
28. 28.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 864 sq cm
29. 29.A cuboid is 8 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 17 cu cm (b) 40 cu cm (c) 184 cu cm (d) 160 cu cm
30. 30.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
31. 31.A cuboid is 8 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 272 sq cm (b) 68 sq cm (c) 96 sq cm (d) 136 sq cm
32. 32.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 512 sq cm (d) 384 sq cm
33. 33.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
34. 34.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 54 cu cm (c) 27 cu cm (d) 9 cu cm
35. 35.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 400 cu cm (d) 30 cu cm
36. 36.A cuboid is 11 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 328 sq cm (b) 656 sq cm (c) 164 sq cm (d) 352 sq cm
37. 37.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
39. 39.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
40. 40.A cuboid is 12 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 282 sq cm (b) 564 sq cm (c) 252 sq cm (d) 141 sq cm

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