Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 684 · 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 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
2. 2.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) 64 times (c) 16 times (d) 8 times
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
5. 5.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 25 sq cm (d) 125 sq cm
6. 6.A cuboid is 10 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 310 cu cm (b) 22 cu cm (c) 350 cu cm (d) 50 cu cm
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
8. 8.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
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
10. 10.A cuboid is 11 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 55 cu cm (b) 275 cu cm (c) 21 cu cm (d) 270 cu cm
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
12. 12.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
13. 13.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
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
15. 15.A cuboid is 9 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 27 cu cm (b) 174 cu cm (c) 17 cu cm (d) 135 cu cm
16. 16.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
17. 17.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
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) 10 times (b) 125 times (c) 5 times (d) 25 times
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
20. 20.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 196 cu cm (c) 294 cu cm (d) 21 cu cm
21. 21.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 24 cu cm (d) 512 cu cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
24. 24.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
25. 25.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 6 cu cm (c) 32 cu cm (d) 12 cu cm
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
27. 27.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
29. 29.A cuboid is 8 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 160 sq cm (b) 232 sq cm (c) 464 sq cm (d) 116 sq cm
30. 30.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 10 cu cm (b) 30 cu cm (c) 31 cu cm (d) 62 cu cm
31. 31.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
32. 32.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 122 cu cm (b) 84 cu cm (c) 14 cu cm (d) 12 cu 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) 8 times (b) 4 times (c) 16 times (d) 64 times
34. 34.A cuboid is 10 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 216 sq cm (b) 180 sq cm (c) 432 sq cm (d) 108 sq cm
35. 35.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 144 cu cm (d) 18 cu cm
36. 36.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
37. 37.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) 5 times (d) 4 times
38. 38.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 12 cu cm (d) 96 cu cm
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
40. 40.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times

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