Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 372 · 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 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
6. 6.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) 5 times (c) 4 times (d) 8 times
7. 7.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
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
9. 9.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) 4 times (c) 16 times (d) 8 times
10. 10.A cuboid is 8 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 752 sq cm (b) 376 sq cm (c) 480 sq cm (d) 188 sq cm
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
13. 13.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
14. 14.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 19 cu cm (b) 228 cu cm (c) 216 cu cm (d) 24 cu cm
15. 15.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
17. 17.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 65 sq cm (c) 32 sq cm (d) 64 sq cm
18. 18.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 64 sq cm (d) 16 sq cm
19. 19.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 108 cu cm (b) 552 cu cm (c) 29 cu cm (d) 864 cu cm
20. 20.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) 25 times (c) 5 times (d) 125 times
21. 21.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 61 sq cm (c) 122 sq cm (d) 244 sq cm
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
23. 23.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
25. 25.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 112 sq cm (b) 172 sq cm (c) 344 sq cm (d) 86 sq cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
27. 27.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 6 cu cm (b) 13 cu cm (c) 48 cu cm (d) 92 cu cm
28. 28.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) 27 times (c) 3 times (d) 9 times
29. 29.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) 64 times (c) 16 times (d) 8 times
30. 30.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) 6 times (c) 27 times (d) 9 times
31. 31.A cuboid is 12 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 144 sq cm (b) 432 sq cm (c) 108 sq cm (d) 216 sq cm
32. 32.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 13 cu cm (b) 72 cu cm (c) 108 cu cm (d) 12 cu cm
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
35. 35.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu cm
36. 36.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
37. 37.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 24 cu cm (b) 9 cu cm (c) 6 cu cm (d) 52 cu cm
38. 38.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
39. 39.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) 9 times (d) 3 times
40. 40.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

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