Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 51 · 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 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
3. 3.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 216 cu cm (d) 217 cu cm
4. 4.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) 6 times (d) 2 times
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
11. 11.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 94 sq cm (b) 188 sq cm (c) 47 sq cm (d) 60 sq cm
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
13. 13.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
14. 14.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) 9 times (c) 6 times (d) 3 times
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
16. 16.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) 8 times (d) 16 times
17. 17.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) 16 times (c) 64 times (d) 4 times
18. 18.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
20. 20.A cuboid is 11 cm long, 9 cm wide and 7 cm high. What is its volume? (a) 478 cu cm (b) 27 cu cm (c) 99 cu cm (d) 693 cu cm
21. 21.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
22. 22.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 17 cu cm (c) 180 cu cm (d) 144 cu cm
23. 23.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
24. 24.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 600 cu cm (d) 1000 cu cm
25. 25.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
28. 28.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) 16 times (c) 64 times (d) 8 times
29. 29.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
30. 30.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 10 cu cm (b) 132 cu cm (c) 80 cu cm (d) 15 cu cm
31. 31.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
32. 32.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 217 sq cm (d) 144 sq cm
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
34. 34.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) 16 times (c) 64 times (d) 8 times
35. 35.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 864 sq cm
36. 36.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
37. 37.A cuboid is 9 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 73 sq cm (b) 292 sq cm (c) 146 sq cm (d) 90 sq cm
38. 38.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 162 sq cm (b) 324 sq cm (c) 81 sq cm (d) 108 sq cm
39. 39.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 276 sq cm (b) 280 sq cm (c) 552 sq cm (d) 138 sq cm
40. 40.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 72 sq cm (c) 32 sq cm (d) 36 sq cm

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