Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 105 · 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) 8 times (b) 4 times (c) 2 times (d) 5 times
2. 2.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) 125 times (c) 10 times (d) 25 times
3. 3.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 484 cu cm (d) 1331 cu cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
5. 5.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 8 cu cm (d) 6 cu cm
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
7. 7.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
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
9. 9.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 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.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
15. 15.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 432 sq cm (b) 180 sq cm (c) 108 sq cm (d) 216 sq cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
17. 17.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 126 cu cm (c) 81 cu cm (d) 27 cu cm
18. 18.A cuboid is 9 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 54 cu cm (b) 258 cu cm (c) 270 cu cm (d) 20 cu cm
19. 19.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 176 sq cm (b) 88 sq cm (c) 48 sq cm (d) 44 sq cm
20. 20.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 6 cu cm (b) 12 cu cm (c) 82 cu cm (d) 42 cu cm
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
22. 22.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
23. 23.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
24. 24.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) 8 times (d) 16 times
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
27. 27.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
28. 28.A cuboid is 11 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 352 sq cm (b) 328 sq cm (c) 164 sq cm (d) 656 sq cm
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
32. 32.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) 5 times (c) 25 times (d) 10 times
33. 33.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) 8 times (d) 2 times
34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
35. 35.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
36. 36.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
37. 37.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 216 cu cm (d) 217 cu cm
38. 38.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 224 sq cm (b) 60 sq cm (c) 56 sq cm (d) 112 sq cm
39. 39.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 124 sq cm (b) 30 sq cm (c) 62 sq cm (d) 31 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) 16 times (b) 8 times (c) 64 times (d) 4 times

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