Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 442 · 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.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) 27 times (d) 6 times
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
3. 3.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) 9 times (c) 27 times (d) 6 times
4. 4.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
5. 5.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
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
7. 7.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
8. 8.A cuboid is 10 cm long, 7 cm wide and 3 cm high. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 242 sq cm (d) 210 sq cm
9. 9.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 204 sq cm (b) 51 sq cm (c) 102 sq cm (d) 63 sq cm
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
12. 12.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
13. 13.A cuboid is 9 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 54 cu cm (c) 102 cu cm (d) 18 cu cm
14. 14.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
16. 16.A cuboid is 10 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 380 sq cm (b) 95 sq cm (c) 190 sq cm (d) 150 sq cm
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
18. 18.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
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
21. 21.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
22. 22.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 68 sq cm (b) 272 sq cm (c) 136 sq cm (d) 80 sq cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
24. 24.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 16 cu cm (d) 24 cu cm
25. 25.A cuboid is 9 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 51 sq cm (b) 204 sq cm (c) 102 sq cm (d) 54 sq cm
26. 26.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 152 sq cm (b) 76 sq cm (c) 40 sq cm (d) 38 sq cm
27. 27.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
28. 28.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
29. 29.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
30. 30.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) 9 times (d) 6 times
31. 31.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
32. 32.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) 4 times (c) 8 times (d) 2 times
33. 33.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
34. 34.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 45 cu cm (c) 78 cu cm (d) 11 cu cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 92 sq cm (c) 184 sq cm (d) 48 sq cm
36. 36.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
38. 38.A cuboid is 12 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 84 cu cm (b) 672 cu cm (c) 27 cu cm (d) 472 cu cm
39. 39.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 8 sq cm (d) 4 sq cm
40. 40.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times

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