Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 908 · 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.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) 3 times (d) 6 times
2. 2.What is the circumference of a circle of diameter 56 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 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
6. 6.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
7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
8. 8.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) 125 times (c) 5 times (d) 25 times
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
13. 13.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 216 cu cm (d) 144 cu cm
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
16. 16.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
17. 17.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
18. 18.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
19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
20. 20.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
21. 21.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
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) 10 times (d) 25 times
23. 23.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 184 sq cm (b) 368 sq cm (c) 92 sq cm (d) 120 sq cm
24. 24.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
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
27. 27.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 512 sq cm (d) 384 sq cm
28. 28.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 486 cu cm (d) 324 cu cm
29. 29.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
30. 30.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) 9 times (c) 6 times (d) 27 times
31. 31.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 96 cu cm (d) 65 cu cm
32. 32.A cuboid is 11 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 25 cu cm (b) 440 cu cm (c) 44 cu cm (d) 388 cu cm
33. 33.A cuboid is 8 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 191 sq cm (b) 764 sq cm (c) 504 sq cm (d) 382 sq cm
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
35. 35.A cuboid is 12 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 784 sq cm (b) 392 sq cm (c) 480 sq cm (d) 196 sq cm
36. 36.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 54 sq cm (d) 36 sq cm
37. 37.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
38. 38.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 6 times (d) 4 times
39. 39.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 200 cu cm (b) 19 cu cm (c) 20 cu cm (d) 220 cu cm
40. 40.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) 10 times (d) 125 times

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