Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 559 · 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 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
3. 3.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
7. 7.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 216 cu cm (d) 217 cu cm
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
11. 11.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 14 cu cm (b) 126 cu cm (c) 18 cu cm (d) 90 cu cm
12. 12.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) 2 times (c) 8 times (d) 6 times
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
15. 15.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
17. 17.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) 125 times (c) 5 times (d) 25 times
18. 18.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
19. 19.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) 8 times (c) 4 times (d) 16 times
20. 20.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 40 cu cm (b) 24 cu cm (c) 360 cu cm (d) 400 cu cm
21. 21.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
22. 22.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) 125 times (c) 25 times (d) 10 times
23. 23.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) 16 times (c) 4 times (d) 8 times
24. 24.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
26. 26.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 336 sq cm (b) 108 sq cm (c) 84 sq cm (d) 168 sq cm
27. 27.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 21 cu cm (b) 180 cu cm (c) 256 cu cm (d) 18 cu 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) 2 times (b) 4 times (c) 8 times (d) 5 times
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
31. 31.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 31 sq cm (b) 62 sq cm (c) 30 sq cm (d) 124 sq cm
32. 32.A cuboid is 7 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 572 sq cm (b) 286 sq cm (c) 143 sq cm (d) 315 sq cm
33. 33.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 76 cu cm (b) 10 cu cm (c) 40 cu cm (d) 11 cu cm
34. 34.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 729 sq cm (d) 486 sq cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
36. 36.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 33 cu cm
37. 37.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 343 cu cm (d) 21 cu cm
38. 38.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) 8 times (c) 5 times (d) 4 times
39. 39.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times

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