Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 517 · 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 radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
3. 3.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
4. 4.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 36 sq cm (d) 144 sq cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
6. 6.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) 64 times (c) 16 times (d) 8 times
7. 7.A cuboid is 8 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 20 cu cm (b) 288 cu cm (c) 264 cu cm (d) 48 cu cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
9. 9.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 484 sq cm (c) 1331 sq cm (d) 121 sq cm
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
11. 11.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
12. 12.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
13. 13.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 54 cu cm (b) 102 cu cm (c) 14 cu cm (d) 6 cu cm
14. 14.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 294 sq cm (d) 196 sq cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 6 cu cm (b) 60 cu cm (c) 112 cu cm (d) 15 cu cm
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
20. 20.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 726 cu cm
21. 21.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 96 cu cm (d) 65 cu cm
22. 22.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 28 cu cm (b) 14 cu cm (c) 11 cu cm (d) 64 cu cm
23. 23.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 24 cu cm (d) 512 cu cm
24. 24.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 64 sq cm (d) 512 sq cm
25. 25.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
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
27. 27.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
29. 29.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) 4 times (c) 8 times (d) 5 times
30. 30.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
31. 31.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
32. 32.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
33. 33.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
34. 34.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) 8 times (c) 5 times (d) 4 times
35. 35.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) 6 times (c) 8 times (d) 4 times
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
37. 37.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 20 cu cm (b) 184 cu cm (c) 17 cu cm (d) 160 cu cm
38. 38.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 368 sq cm (b) 92 sq cm (c) 184 sq cm (d) 160 sq cm
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times

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