Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 850 · 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 diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
6. 6.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
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
8. 8.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 150 sq cm (d) 125 sq cm
9. 9.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
12. 12.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 30 cu cm
13. 13.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
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
15. 15.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
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
17. 17.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
18. 18.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
20. 20.A cuboid is 11 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 22 cu cm (b) 33 cu cm (c) 290 cu cm (d) 264 cu cm
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
23. 23.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 12 cu cm (b) 150 cu cm (c) 16 cu cm (d) 108 cu cm
24. 24.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
26. 26.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 118 sq cm (b) 236 sq cm (c) 70 sq cm (d) 59 sq cm
28. 28.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
29. 29.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) 3 times (c) 27 times (d) 6 times
30. 30.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
31. 31.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 81 sq cm (d) 486 sq cm
32. 32.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
33. 33.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
34. 34.A cuboid is 9 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 504 sq cm (b) 191 sq cm (c) 382 sq cm (d) 764 sq cm
35. 35.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) 5 times (c) 25 times (d) 125 times
36. 36.A cuboid is 9 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 159 sq cm (b) 318 sq cm (c) 378 sq cm (d) 636 sq cm
37. 37.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 148 sq cm (b) 296 sq cm (c) 120 sq cm (d) 74 sq cm
38. 38.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 36 sq cm (b) 132 sq cm (c) 66 sq cm (d) 33 sq cm
39. 39.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 270 sq cm (b) 258 sq cm (c) 516 sq cm (d) 129 sq cm
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm

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