Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 875 · 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 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 54 cu cm (d) 27 cu cm
2. 2.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 39 sq cm (b) 78 sq cm (c) 45 sq cm (d) 156 sq cm
3. 3.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
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
5. 5.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
6. 6.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 81 sq cm (b) 162 sq cm (c) 126 sq cm (d) 324 sq cm
7. 7.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) 8 times (c) 2 times (d) 6 times
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
9. 9.A cuboid is 11 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 28 cu cm (b) 99 cu cm (c) 518 cu cm (d) 792 cu cm
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
12. 12.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 24 cu cm (d) 16 cu cm
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
16. 16.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 726 sq cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
18. 18.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 726 cu cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
20. 20.A cuboid is 11 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 165 sq cm (b) 206 sq cm (c) 412 sq cm (d) 103 sq cm
21. 21.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
22. 22.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) 27 times (d) 9 times
23. 23.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
24. 24.A cuboid is 8 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 132 sq cm (b) 66 sq cm (c) 264 sq cm (d) 80 sq cm
25. 25.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) 2 times (c) 5 times (d) 4 times
26. 26.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 190 cu cm (b) 150 cu cm (c) 15 cu cm (d) 18 cu cm
27. 27.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
28. 28.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 36 cu cm (c) 162 cu cm (d) 108 cu cm
29. 29.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 576 cu cm
30. 30.A cuboid is 9 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 174 cu cm (b) 17 cu cm (c) 27 cu cm (d) 135 cu cm
31. 31.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 1728 sq cm (c) 576 sq cm (d) 864 sq cm
32. 32.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
33. 33.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 190 cu cm (b) 126 cu cm (c) 127 cu cm (d) 18 cu cm
34. 34.A cuboid is 11 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 330 sq cm (b) 151 sq cm (c) 604 sq cm (d) 302 sq cm
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
36. 36.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
37. 37.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
38. 38.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 36 cu cm (b) 11 cu cm (c) 12 cu cm (d) 72 cu cm
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
40. 40.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

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