Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 955 · 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 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
2. 2.A cuboid is 9 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 150 sq cm (b) 300 sq cm (c) 108 sq cm (d) 75 sq cm
3. 3.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
6. 6.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 56 cu cm (b) 13 cu cm (c) 100 cu cm (d) 8 cu cm
7. 7.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 400 sq cm (d) 1000 sq cm
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
9. 9.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 196 cu cm (d) 294 cu cm
10. 10.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 20 cu cm (c) 60 cu cm (d) 12 cu cm
11. 11.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 81 cu cm (c) 27 cu cm (d) 126 cu cm
12. 12.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 56 sq cm (c) 80 sq cm (d) 112 sq cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 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) 2 times (b) 4 times (c) 8 times (d) 5 times
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
18. 18.A cuboid is 12 cm long, 11 cm wide and 3 cm high. What is its volume? (a) 402 cu cm (b) 132 cu cm (c) 26 cu cm (d) 396 cu cm
19. 19.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 88 sq cm (c) 44 sq cm (d) 176 sq cm
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
21. 21.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
22. 22.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
23. 23.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
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
25. 25.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
26. 26.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
27. 27.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm
28. 28.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 68 sq cm (b) 272 sq cm (c) 84 sq cm (d) 136 sq cm
29. 29.A cuboid is 10 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 60 cu cm (b) 240 cu cm (c) 20 cu cm (d) 248 cu 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 radius of a circle 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
32. 32.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 136 sq cm (b) 68 sq cm (c) 80 sq cm (d) 272 sq cm
33. 33.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 36 cu cm
34. 34.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 27 cu cm (d) 36 cu cm
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
36. 36.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 216 cu cm (d) 144 cu cm
37. 37.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
38. 38.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
39. 39.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
40. 40.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

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