Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 622 · 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.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 125 cu cm (d) 150 cu cm
2. 2.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 8 cu cm (b) 9 cu cm (c) 52 cu cm (d) 24 cu cm
3. 3.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
4. 4.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
5. 5.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
7. 7.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) 124 sq cm (d) 30 sq cm
8. 8.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
9. 9.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 49 sq cm (d) 343 sq cm
10. 10.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 600 cu cm (d) 1000 cu cm
11. 11.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
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
13. 13.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) 5 times (c) 125 times (d) 10 times
14. 14.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 172 cu cm (b) 56 cu cm (c) 17 cu cm (d) 112 cu cm
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
16. 16.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
17. 17.A cuboid is 11 cm long, 10 cm wide and 2 cm high. What is its total surface area? (a) 152 sq cm (b) 220 sq cm (c) 608 sq cm (d) 304 sq cm
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
19. 19.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
20. 20.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 8 cu cm (b) 64 cu cm (c) 14 cu cm (d) 112 cu cm
21. 21.A cuboid is 8 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 292 cu cm (b) 48 cu cm (c) 336 cu cm (d) 21 cu cm
22. 22.A cuboid is 12 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 564 sq cm (b) 252 sq cm (c) 141 sq cm (d) 282 sq cm
23. 23.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
25. 25.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) 4 times (d) 5 times
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 384 sq cm (d) 512 sq cm
27. 27.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 21 cu cm (d) 196 cu cm
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
29. 29.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
30. 30.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
31. 31.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) 10 times (c) 25 times (d) 125 times
32. 32.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
33. 33.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) 8 times (d) 4 times
34. 34.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 8 sq cm (c) 16 sq cm (d) 4 sq cm
35. 35.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 384 cu cm (d) 256 cu cm
36. 36.A cuboid is 12 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 468 cu cm (b) 72 cu cm (c) 27 cu cm (d) 648 cu cm
37. 37.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
38. 38.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 188 sq cm (b) 47 sq cm (c) 60 sq cm (d) 94 sq cm
39. 39.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) 16 times (c) 64 times (d) 4 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) 4 times (b) 8 times (c) 64 times (d) 16 times

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