Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 102 · 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) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
3. 3.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
4. 4.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
5. 5.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
6. 6.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 150 sq cm (b) 75 sq cm (c) 300 sq cm (d) 108 sq cm
7. 7.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 254 cu cm (b) 20 cu cm (c) 28 cu cm (d) 252 cu cm
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
9. 9.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
10. 10.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 484 cu cm (d) 1331 cu cm
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
13. 13.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
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
15. 15.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) 8 times (c) 64 times (d) 4 times
16. 16.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 384 cu cm (d) 24 cu cm
17. 17.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 1728 cu cm (c) 36 cu cm (d) 576 cu cm
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
20. 20.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
21. 21.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
22. 22.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) 6 times (c) 3 times (d) 9 times
23. 23.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 150 sq cm (c) 100 sq cm (d) 125 sq cm
24. 24.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 21 cu cm (b) 180 cu cm (c) 256 cu cm (d) 18 cu cm
25. 25.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 36 sq cm (d) 9 sq cm
26. 26.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 729 sq cm (d) 81 sq cm
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
29. 29.A cuboid is 6 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 60 cu cm (b) 12 cu cm (c) 13 cu cm (d) 104 cu cm
30. 30.A cuboid is 12 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 21 cu cm (b) 168 cu cm (c) 244 cu cm (d) 84 cu cm
31. 31.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) 27 times (c) 6 times (d) 9 times
32. 32.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
33. 33.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
34. 34.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 84 cu cm (b) 136 cu cm (c) 12 cu cm (d) 15 cu cm
35. 35.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
36. 36.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 92 cu cm (b) 6 cu cm (c) 48 cu cm (d) 13 cu cm
37. 37.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 216 cu cm (d) 18 cu cm
38. 38.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 27 cu cm (d) 486 cu cm
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
40. 40.A cuboid is 10 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 112 cu cm (b) 20 cu cm (c) 15 cu cm (d) 60 cu cm

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