Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 89 · 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 every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
3. 3.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
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 400 sq cm (d) 1000 sq cm
6. 6.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
7. 7.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) 6 times (c) 2 times (d) 8 times
8. 8.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) 8 times (c) 4 times (d) 64 times
9. 9.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 216 cu cm (d) 217 cu cm
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
13. 13.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
14. 14.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm
15. 15.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 63 cu cm (c) 190 cu cm (d) 126 cu cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
17. 17.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 54 sq cm (d) 27 sq cm
18. 18.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
20. 20.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
21. 21.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
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
23. 23.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 31 sq cm (b) 30 sq cm (c) 62 sq cm (d) 124 sq cm
24. 24.A cuboid is 7 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 94 sq cm (b) 188 sq cm (c) 376 sq cm (d) 168 sq cm
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
26. 26.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 100 cu cm (c) 160 cu cm (d) 50 cu cm
27. 27.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
28. 28.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
29. 29.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) 2 times (d) 8 times
30. 30.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 112 cu cm (c) 6 cu cm (d) 60 cu cm
31. 31.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
32. 32.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) 9 times (c) 27 times (d) 6 times
33. 33.A cuboid is 9 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 258 sq cm (b) 129 sq cm (c) 516 sq cm (d) 270 sq cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 17 cu cm (d) 40 cu cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 82 sq cm (b) 164 sq cm (c) 42 sq cm (d) 41 sq cm
36. 36.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 52 cu cm (b) 9 cu cm (c) 24 cu cm (d) 6 cu cm
38. 38.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
40. 40.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times

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