Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 524 · 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) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
3. 3.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
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
5. 5.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
6. 6.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 9 cu cm (b) 24 cu cm (c) 52 cu cm (d) 6 cu cm
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
9. 9.If the side of a square 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
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
12. 12.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
14. 14.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 65 sq cm (b) 128 sq cm (c) 64 sq cm (d) 32 sq cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
16. 16.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
17. 17.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
18. 18.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
19. 19.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
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
21. 21.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 344 sq cm (b) 172 sq cm (c) 86 sq cm (d) 112 sq cm
22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
23. 23.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
24. 24.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
25. 25.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 100 sq cm (c) 400 sq cm (d) 600 sq cm
26. 26.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
28. 28.A cuboid is 8 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 68 sq cm (b) 136 sq cm (c) 96 sq cm (d) 272 sq cm
29. 29.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
30. 30.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
31. 31.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 400 cu cm (d) 1000 cu cm
32. 32.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
33. 33.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 294 sq cm (d) 49 sq cm
34. 34.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 64 cu cm (d) 12 cu cm
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
36. 36.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 8 cu cm (d) 18 cu cm
37. 37.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 217 sq cm (d) 144 sq cm
38. 38.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its volume? (a) 294 cu cm (b) 90 cu cm (c) 22 cu cm (d) 270 cu cm
39. 39.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
40. 40.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) 16 times (c) 4 times (d) 8 times

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