Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 669 · 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 radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
2. 2.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
3. 3.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 150 cu cm (d) 125 cu cm
4. 4.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
5. 5.A cuboid is 6 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 108 cu cm (b) 72 cu cm (c) 18 cu cm (d) 13 cu cm
6. 6.If the radius of a circle 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
7. 7.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) 4 times (c) 5 times (d) 8 times
8. 8.A cuboid is 6 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 17 cu cm (b) 180 cu cm (c) 192 cu cm (d) 30 cu cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 30 sq cm (d) 31 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
12. 12.A cuboid is 8 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 131 sq cm (b) 280 sq cm (c) 524 sq cm (d) 262 sq cm
13. 13.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
16. 16.A cuboid is 6 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 128 sq cm (d) 96 sq cm
17. 17.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
19. 19.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 21 cu cm (b) 202 cu cm (c) 168 cu cm (d) 18 cu cm
20. 20.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) 4 times (c) 64 times (d) 16 times
21. 21.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
22. 22.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
23. 23.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm
24. 24.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) 8 times (c) 4 times (d) 2 times
25. 25.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
26. 26.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 508 sq cm (b) 252 sq cm (c) 254 sq cm (d) 127 sq cm
27. 27.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
28. 28.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) 27 times (c) 6 times (d) 9 times
29. 29.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
30. 30.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
31. 31.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
32. 32.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
33. 33.A cuboid is 8 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 224 sq cm (b) 464 sq cm (c) 116 sq cm (d) 232 sq cm
34. 34.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
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
36. 36.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) 10 times (c) 125 times (d) 5 times
37. 37.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
38. 38.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 14 cu cm (b) 15 cu cm (c) 136 cu cm (d) 84 cu cm
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
40. 40.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm

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