Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 205 · 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 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
3. 3.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
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 circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
7. 7.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
8. 8.A cuboid is 11 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 132 sq cm (b) 100 sq cm (c) 200 sq cm (d) 400 sq cm
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
10. 10.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 36 cu cm (d) 9 cu cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
12. 12.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
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
15. 15.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 30 sq cm (c) 31 sq cm (d) 62 sq cm
16. 16.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
18. 18.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 16 sq cm (c) 64 sq cm (d) 32 sq cm
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
21. 21.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 8 cu cm (c) 16 cu cm (d) 40 cu cm
22. 22.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
23. 23.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
24. 24.A cuboid is 12 cm long, 9 cm wide and 6 cm high. What is its total surface area? (a) 234 sq cm (b) 468 sq cm (c) 936 sq cm (d) 648 sq cm
25. 25.A cuboid is 7 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 98 sq cm (b) 308 sq cm (c) 77 sq cm (d) 154 sq cm
26. 26.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
28. 28.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) 5 times (c) 125 times (d) 10 times
29. 29.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 184 sq cm (b) 48 sq cm (c) 46 sq cm (d) 92 sq cm
30. 30.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) 25 times (c) 10 times (d) 125 times
31. 31.A cuboid is 11 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 693 sq cm (b) 478 sq cm (c) 239 sq cm (d) 956 sq cm
32. 32.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) 6 times (c) 9 times (d) 27 times
33. 33.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) 25 times (c) 5 times (d) 10 times
34. 34.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 82 cu cm (c) 6 cu cm (d) 42 cu cm
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
36. 36.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 216 cu cm (d) 144 cu cm
37. 37.A cuboid is 7 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 172 sq cm (b) 344 sq cm (c) 112 sq cm (d) 86 sq cm
38. 38.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
39. 39.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 72 cu cm (b) 12 cu cm (c) 36 cu cm (d) 11 cu cm
40. 40.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 20 cu cm (c) 48 cu cm (d) 10 cu cm

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