Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 215 · 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 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
2. 2.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) 2 times (c) 4 times (d) 8 times
3. 3.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 65 cu cm (d) 12 cu cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
6. 6.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
7. 7.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
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
9. 9.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
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
11. 11.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
12. 12.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 1728 cu cm (c) 576 cu cm (d) 36 cu cm
13. 13.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 512 cu cm (d) 384 cu cm
14. 14.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
17. 17.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
18. 18.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 112 cu cm (b) 64 cu cm (c) 14 cu cm (d) 32 cu cm
19. 19.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
20. 20.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) 25 times (c) 10 times (d) 5 times
21. 21.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 300 sq cm (b) 75 sq cm (c) 108 sq cm (d) 150 sq cm
22. 22.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
23. 23.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 125 sq cm (d) 150 sq cm
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq 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) 8 times (b) 16 times (c) 4 times (d) 64 times
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
28. 28.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 68 sq cm (b) 96 sq cm (c) 272 sq cm (d) 136 sq cm
29. 29.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 104 cu cm (b) 30 cu cm (c) 60 cu cm (d) 13 cu cm
30. 30.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
31. 31.A cuboid is 8 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 202 cu cm (b) 168 cu cm (c) 18 cu cm (d) 56 cu cm
32. 32.A cuboid is 9 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 45 cu cm (b) 225 cu cm (c) 230 cu cm (d) 19 cu cm
33. 33.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 54 sq cm (d) 36 sq cm
34. 34.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
35. 35.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
36. 36.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
37. 37.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
38. 38.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 121 sq cm
39. 39.A cuboid is 11 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 960 sq cm (b) 704 sq cm (c) 240 sq cm (d) 480 sq cm
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times

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