Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 178 · 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 area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
2. 2.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 13 cu cm (b) 10 cu cm (c) 104 cu cm (d) 60 cu cm
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
4. 4.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 729 sq cm (c) 81 sq cm (d) 324 sq cm
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
6. 6.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) 64 times (c) 16 times (d) 4 times
7. 7.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) 8 times (c) 2 times (d) 4 times
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
11. 11.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
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
13. 13.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) 8 times (c) 4 times (d) 64 times
14. 14.A cuboid is 7 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 332 sq cm (b) 140 sq cm (c) 166 sq cm (d) 83 sq cm
15. 15.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
16. 16.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 272 sq cm (b) 68 sq cm (c) 136 sq cm (d) 84 sq cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 6 cu cm (b) 72 cu cm (c) 11 cu cm (d) 36 cu cm
18. 18.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq 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) 6 times (b) 2 times (c) 8 times (d) 4 times
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
22. 22.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 144 sq cm (d) 216 sq cm
23. 23.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
24. 24.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 8 cu cm (d) 6 cu cm
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
26. 26.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 136 cu cm (b) 96 cu cm (c) 12 cu cm (d) 15 cu cm
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 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) 27 times (c) 6 times (d) 3 times
29. 29.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 144 sq cm
30. 30.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu cm
31. 31.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
32. 32.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
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
34. 34.A cuboid is 11 cm long, 9 cm wide and 7 cm high. What is its volume? (a) 27 cu cm (b) 478 cu cm (c) 99 cu cm (d) 693 cu cm
35. 35.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
36. 36.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 16 sq cm (d) 97 sq cm
37. 37.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
38. 38.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 96 cu cm (c) 160 cu cm (d) 18 cu cm
39. 39.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
40. 40.A cuboid is 12 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 23 cu cm (b) 216 cu cm (c) 300 cu cm (d) 108 cu cm

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