Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 854 · 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) 220 cm (d) 110 cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 30 sq cm (b) 124 sq cm (c) 31 sq cm (d) 62 sq cm
4. 4.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
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.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
8. 8.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
9. 9.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) 25 times (c) 10 times (d) 125 times
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
12. 12.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) 5 times (c) 10 times (d) 125 times
13. 13.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 270 sq cm (b) 540 sq cm (c) 243 sq cm (d) 135 sq cm
14. 14.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
15. 15.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
16. 16.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
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
18. 18.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) 5 times (c) 4 times (d) 2 times
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
20. 20.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 108 sq cm (c) 75 sq cm (d) 300 sq cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
22. 22.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 324 cu cm (d) 27 cu cm
23. 23.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
24. 24.A cuboid is 9 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 99 sq cm (b) 396 sq cm (c) 198 sq cm (d) 162 sq cm
25. 25.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
27. 27.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 64 sq cm (d) 96 sq cm
28. 28.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) 2 times (c) 5 times (d) 4 times
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
30. 30.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 90 cu cm (c) 50 cu cm (d) 12 cu cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 24 sq cm (b) 104 sq cm (c) 52 sq cm (d) 26 sq cm
32. 32.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 36 cu cm
33. 33.A cuboid is 7 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 315 sq cm (b) 572 sq cm (c) 286 sq cm (d) 143 sq cm
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
35. 35.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
36. 36.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
37. 37.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
38. 38.A cuboid is 12 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 282 cu cm (b) 252 cu cm (c) 22 cu cm (d) 84 cu cm
39. 39.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
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm

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