Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 951 · 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.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 42 sq cm (c) 21 sq cm (d) 84 sq cm
2. 2.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 864 cu cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
6. 6.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
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
8. 8.A cuboid is 7 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 166 sq cm (b) 332 sq cm (c) 140 sq cm (d) 83 sq cm
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
10. 10.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 84 sq cm (b) 272 sq cm (c) 68 sq cm (d) 136 sq cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
12. 12.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
13. 13.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) 27 times (d) 9 times
14. 14.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 9 cu cm (d) 52 cu cm
15. 15.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) 25 times (c) 125 times (d) 10 times
16. 16.A cuboid is 11 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 88 cu cm (b) 616 cu cm (c) 442 cu cm (d) 26 cu cm
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
18. 18.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
22. 22.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
23. 23.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
24. 24.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
25. 25.A cuboid is 10 cm long, 8 cm wide and 6 cm high. What is its volume? (a) 376 cu cm (b) 24 cu cm (c) 480 cu cm (d) 80 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) 25 times (b) 125 times (c) 5 times (d) 10 times
27. 27.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) 2 times (c) 5 times (d) 4 times
28. 28.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
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
30. 30.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 76 cu cm (b) 11 cu cm (c) 10 cu cm (d) 40 cu cm
31. 31.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
33. 33.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) 27 times (c) 3 times (d) 9 times
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
35. 35.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 16 cu cm (b) 136 cu cm (c) 80 cu cm (d) 8 cu cm
36. 36.A cuboid is 11 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 99 cu cm (b) 22 cu cm (c) 198 cu cm (d) 278 cu cm
37. 37.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
38. 38.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
39. 39.A cuboid is 11 cm long, 10 cm wide and 7 cm high. What is its volume? (a) 110 cu cm (b) 28 cu cm (c) 514 cu cm (d) 770 cu cm
40. 40.A cuboid is 7 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 464 sq cm (b) 232 sq cm (c) 224 sq cm (d) 116 sq cm

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