Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 989 · 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 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
4. 4.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
5. 5.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
6. 6.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
7. 7.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
9. 9.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 292 sq cm (b) 90 sq cm (c) 73 sq cm (d) 146 sq cm
10. 10.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) 27 times (c) 9 times (d) 6 times
11. 11.If the radius of a circle 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
12. 12.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 36 cu cm (d) 9 cu cm
13. 13.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 92 cu cm (b) 13 cu cm (c) 48 cu cm (d) 6 cu cm
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
15. 15.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
16. 16.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
17. 17.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) 2 times (c) 4 times (d) 5 times
18. 18.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 202 sq cm (b) 180 sq cm (c) 404 sq cm (d) 101 sq cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
20. 20.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) 5 times (c) 125 times (d) 10 times
21. 21.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
22. 22.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
23. 23.A cuboid is 12 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 236 sq cm (b) 944 sq cm (c) 672 sq cm (d) 472 sq cm
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
25. 25.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
26. 26.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 24 cu cm (d) 16 cu cm
27. 27.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
30. 30.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 54 sq cm (d) 9 sq cm
31. 31.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
32. 32.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
33. 33.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) 8 times (d) 4 times
34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
35. 35.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
36. 36.A cuboid is 9 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 143 sq cm (b) 315 sq cm (c) 572 sq cm (d) 286 sq cm
37. 37.A cuboid is 10 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 224 sq cm (b) 60 sq cm (c) 56 sq cm (d) 112 sq cm
38. 38.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
39. 39.A cuboid is 8 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 184 sq cm (b) 160 sq cm (c) 92 sq cm (d) 368 sq cm
40. 40.A cuboid is 12 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 360 sq cm (b) 162 sq cm (c) 324 sq cm (d) 648 sq cm

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