Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 856 · 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 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
4. 4.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
5. 5.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
6. 6.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 36 sq cm (b) 132 sq cm (c) 33 sq cm (d) 66 sq cm
7. 7.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
8. 8.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 172 cu cm (b) 17 cu cm (c) 56 cu cm (d) 112 cu cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
10. 10.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) 5 times (c) 25 times (d) 10 times
11. 11.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) 8 times (d) 16 times
12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
13. 13.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 108 cu cm (b) 168 cu cm (c) 17 cu cm (d) 54 cu cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
15. 15.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
16. 16.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 19 cu cm (b) 18 cu cm (c) 212 cu cm (d) 144 cu cm
17. 17.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm
18. 18.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) 8 times (d) 4 times
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
21. 21.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 5 times (c) 10 times (d) 25 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) 25 times (d) 10 times
23. 23.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
24. 24.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) 8 times (d) 4 times
25. 25.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 24 cu cm (d) 6 cu cm
26. 26.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
28. 28.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 26 sq cm (b) 52 sq cm (c) 24 sq cm (d) 104 sq cm
29. 29.A cuboid is 8 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 304 cu cm (b) 22 cu cm (c) 32 cu cm (d) 320 cu cm
30. 30.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
31. 31.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
32. 32.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 990 sq cm (b) 598 sq cm (c) 299 sq cm (d) 1196 sq cm
33. 33.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 64 sq cm (d) 256 sq cm
34. 34.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
35. 35.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
36. 36.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
37. 37.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 729 cu cm (c) 27 cu cm (d) 324 cu cm
38. 38.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 68 sq cm (b) 136 sq cm (c) 272 sq cm (d) 84 sq cm
39. 39.A cuboid is 11 cm long, 9 cm wide and 6 cm high. What is its volume? (a) 99 cu cm (b) 438 cu cm (c) 26 cu cm (d) 594 cu cm
40. 40.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 54 cu cm (c) 9 cu cm (d) 27 cu cm

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