Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 426 · 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 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
6. 6.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 100 cu cm (d) 150 cu 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) 125 times (c) 10 times (d) 5 times
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
9. 9.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 324 sq cm (d) 729 sq cm
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
12. 12.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) 5 times (c) 8 times (d) 4 times
13. 13.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) 9 times (c) 3 times (d) 27 times
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
15. 15.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
16. 16.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 8 cu cm (d) 16 cu cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 30 sq cm (d) 31 sq cm
18. 18.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) 64 times (d) 16 times
19. 19.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 50 sq cm (b) 180 sq cm (c) 90 sq cm (d) 45 sq cm
20. 20.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
21. 21.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
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
23. 23.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 343 sq cm (c) 196 sq cm (d) 294 sq cm
24. 24.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 54 sq cm (d) 36 sq cm
25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 97 sq cm (d) 96 sq cm
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
27. 27.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 144 sq cm (d) 36 sq cm
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 64 sq cm (b) 12 sq cm (c) 16 sq cm (d) 32 sq cm
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
31. 31.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
32. 32.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 100 sq cm (b) 200 sq cm (c) 56 sq cm (d) 50 sq cm
33. 33.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
34. 34.A cuboid is 12 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 84 cu cm (b) 252 cu cm (c) 22 cu cm (d) 282 cu cm
35. 35.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) 125 times (c) 5 times (d) 10 times
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
38. 38.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
40. 40.A cuboid is 10 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 752 sq cm (b) 480 sq cm (c) 376 sq cm (d) 188 sq cm

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