Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 750 · 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.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
3. 3.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
5. 5.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) 2 times (c) 8 times (d) 6 times
6. 6.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
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
8. 8.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 54 cu cm (d) 36 cu cm
9. 9.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
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.A cuboid is 11 cm long, 8 cm wide and 5 cm high. What is its total surface area? (a) 366 sq cm (b) 732 sq cm (c) 183 sq cm (d) 440 sq cm
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
14. 14.A cuboid is 11 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 252 sq cm (b) 126 sq cm (c) 504 sq cm (d) 176 sq cm
15. 15.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
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
18. 18.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 sq cm
19. 19.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
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
22. 22.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
23. 23.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
25. 25.A cuboid is 7 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 189 sq cm (b) 111 sq cm (c) 222 sq cm (d) 444 sq 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) 125 times (b) 10 times (c) 25 times (d) 5 times
27. 27.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 222 cu cm (b) 27 cu cm (c) 19 cu cm (d) 189 cu cm
28. 28.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
29. 29.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
30. 30.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
32. 32.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 66 sq cm (c) 132 sq cm (d) 80 sq cm
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
35. 35.A cuboid is 11 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 770 sq cm (b) 1028 sq cm (c) 257 sq cm (d) 514 sq cm
36. 36.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 62 cu cm (b) 30 cu cm (c) 31 cu cm (d) 10 cu cm
37. 37.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 13 cu cm (b) 104 cu cm (c) 60 cu cm (d) 30 cu cm
38. 38.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
39. 39.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 4 sq cm (d) 8 sq cm
40. 40.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) 5 times (c) 125 times (d) 10 times

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