Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 830 · 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 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
2. 2.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 15 cu cm (d) 125 cu cm
3. 3.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
5. 5.If the radius of a circle 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
6. 6.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 92 sq cm (b) 368 sq cm (c) 184 sq cm (d) 120 sq cm
7. 7.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 42 sq cm (c) 164 sq cm (d) 82 sq cm
8. 8.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
11. 11.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
13. 13.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
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
15. 15.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 64 sq cm (c) 256 sq cm (d) 512 sq cm
16. 16.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
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
19. 19.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 8 cu cm (c) 48 cu cm (d) 88 cu cm
20. 20.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) 4 times (c) 6 times (d) 8 times
21. 21.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
23. 23.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 31 sq cm (c) 30 sq cm (d) 62 sq cm
24. 24.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
25. 25.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) 9 times (c) 27 times (d) 3 times
26. 26.A cuboid is 6 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 168 cu cm (b) 17 cu cm (c) 12 cu cm (d) 108 cu cm
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 324 sq cm (d) 486 sq cm
28. 28.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 726 cu cm
29. 29.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
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
31. 31.A cuboid is 8 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 264 sq cm (b) 132 sq cm (c) 66 sq cm (d) 80 sq cm
32. 32.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
33. 33.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 1728 cu cm (c) 864 cu cm (d) 36 cu cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 16 cu cm (b) 80 cu cm (c) 136 cu cm (d) 8 cu cm
35. 35.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 24 cu cm (b) 180 cu cm (c) 144 cu cm (d) 17 cu cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 12 cu cm (b) 17 cu cm (c) 120 cu cm (d) 164 cu cm
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
38. 38.A cuboid is 12 cm long, 11 cm wide and 4 cm high. What is its volume? (a) 528 cu cm (b) 27 cu cm (c) 448 cu cm (d) 132 cu cm
39. 39.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
40. 40.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times

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