Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 594 · 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 cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 142 cu cm (b) 105 cu cm (c) 106 cu cm (d) 15 cu cm
2. 2.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
3. 3.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) 10 times (c) 25 times (d) 125 times
4. 4.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
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
6. 6.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 81 sq cm (d) 729 sq cm
7. 7.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 84 sq cm (c) 42 sq cm (d) 18 sq cm
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
12. 12.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 8 cu cm (c) 48 cu cm (d) 88 cu cm
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
14. 14.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
16. 16.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 716 sq cm (b) 179 sq cm (c) 396 sq cm (d) 358 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
18. 18.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) 25 times (d) 10 times
19. 19.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
20. 20.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) 10 times (c) 5 times (d) 125 times
21. 21.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 48 cu cm (b) 6 cu cm (c) 92 cu cm (d) 13 cu cm
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
24. 24.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 294 sq cm (d) 49 sq cm
25. 25.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
26. 26.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
28. 28.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) 125 times (d) 25 times
29. 29.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 123 sq cm (b) 216 sq cm (c) 492 sq cm (d) 246 sq cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
31. 31.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
32. 32.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 60 cu cm (b) 112 cu cm (c) 6 cu cm (d) 15 cu cm
33. 33.A cuboid is 12 cm long, 11 cm wide and 9 cm high. What is its total surface area? (a) 1188 sq cm (b) 1356 sq cm (c) 339 sq cm (d) 678 sq cm
34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
35. 35.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
36. 36.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 576 sq cm
37. 37.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
38. 38.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 168 sq cm (b) 188 sq cm (c) 376 sq cm (d) 94 sq cm
39. 39.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
40. 40.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm

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