Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 923 · 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 surface area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
3. 3.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 12 cu cm (c) 24 cu cm (d) 88 cu cm
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
5. 5.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 343 cu cm (d) 294 cu cm
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
7. 7.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
8. 8.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) 125 times (c) 25 times (d) 10 times
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
10. 10.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) 6 times (c) 8 times (d) 2 times
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
16. 16.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
17. 17.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) 16 times (c) 64 times (d) 8 times
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
20. 20.A cuboid is 12 cm long, 10 cm wide and 5 cm high. What is its total surface area? (a) 920 sq cm (b) 460 sq cm (c) 230 sq cm (d) 600 sq cm
21. 21.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 36 cu cm (d) 1728 cu cm
22. 22.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 343 sq cm (d) 294 sq cm
23. 23.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
25. 25.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) 10 times (c) 25 times (d) 5 times
26. 26.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 1331 sq cm (c) 121 sq cm (d) 726 sq cm
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
29. 29.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
30. 30.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 125 cu cm (d) 100 cu cm
31. 31.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 216 cu cm (d) 18 cu cm
32. 32.A cuboid is 7 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 147 cu cm (b) 21 cu cm (c) 182 cu cm (d) 17 cu cm
33. 33.A cuboid is 12 cm long, 8 cm wide and 10 cm high. What is its total surface area? (a) 1184 sq cm (b) 592 sq cm (c) 296 sq cm (d) 960 sq cm
34. 34.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
35. 35.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq 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) 25 times (b) 10 times (c) 125 times (d) 5 times
37. 37.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
38. 38.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 164 sq cm (b) 41 sq cm (c) 42 sq cm (d) 82 sq cm
39. 39.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 12 sq cm (c) 32 sq cm (d) 64 sq cm
40. 40.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 9 sq cm (d) 27 sq cm

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