Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 870 · 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) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
2. 2.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
3. 3.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
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
5. 5.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
6. 6.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) 9 times (c) 6 times (d) 27 times
7. 7.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 32 cu cm (c) 12 cu cm (d) 72 cu cm
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
12. 12.If the side of a square 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
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
15. 15.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
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
17. 17.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 144 cu cm (d) 18 cu cm
18. 18.A cuboid is 7 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 142 sq cm (b) 105 sq cm (c) 71 sq cm (d) 284 sq cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
20. 20.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) 6 times (c) 9 times (d) 27 times
21. 21.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 36 cu cm (b) 12 cu cm (c) 72 cu cm (d) 11 cu cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
23. 23.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 36 sq cm (d) 9 sq cm
24. 24.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) 8 times (c) 4 times (d) 2 times
25. 25.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 12 cu cm (d) 64 cu cm
26. 26.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
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
28. 28.A cuboid is 11 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 268 sq cm (b) 536 sq cm (c) 134 sq cm (d) 264 sq cm
29. 29.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) 125 times (c) 5 times (d) 25 times
30. 30.A cuboid is 11 cm long, 10 cm wide and 2 cm high. What is its volume? (a) 110 cu cm (b) 304 cu cm (c) 23 cu cm (d) 220 cu cm
31. 31.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its total surface area? (a) 276 sq cm (b) 552 sq cm (c) 864 sq cm (d) 1104 sq cm
32. 32.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm
33. 33.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) 4 times (c) 8 times (d) 64 times
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
37. 37.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 90 cu cm (b) 14 cu cm (c) 18 cu cm (d) 126 cu cm
38. 38.A cuboid is 7 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 380 sq cm (b) 95 sq cm (c) 190 sq cm (d) 175 sq cm
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
40. 40.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) 4 times (c) 5 times (d) 2 times

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