Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 636 · 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 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
2. 2.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
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
5. 5.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
6. 6.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) 16 times (c) 4 times (d) 64 times
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 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) 5 times (b) 125 times (c) 10 times (d) 25 times
9. 9.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 864 cu cm (b) 552 cu cm (c) 108 cu cm (d) 29 cu cm
10. 10.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
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
14. 14.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
15. 15.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) 10 times (d) 5 times
16. 16.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) 6 times (d) 9 times
17. 17.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
18. 18.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) 8 times (c) 64 times (d) 16 times
19. 19.A cuboid is 8 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 240 cu cm (b) 48 cu cm (c) 236 cu cm (d) 19 cu cm
20. 20.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
21. 21.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 72 sq cm (d) 248 sq cm
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
23. 23.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
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
25. 25.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
26. 26.A cuboid is 8 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 24 cu cm (b) 158 cu cm (c) 16 cu cm (d) 120 cu cm
27. 27.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
28. 28.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 125 sq cm (c) 25 sq cm (d) 100 sq cm
29. 29.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
30. 30.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
31. 31.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 6 cu cm (d) 8 cu cm
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
33. 33.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
34. 34.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 144 sq cm
35. 35.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
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) 8 times (b) 4 times (c) 64 times (d) 16 times
37. 37.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 38 sq cm (b) 40 sq cm (c) 152 sq cm (d) 76 sq cm
38. 38.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) 5 times (c) 25 times (d) 125 times
39. 39.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
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) 125 times (b) 5 times (c) 10 times (d) 25 times

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