Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 266 · 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 area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
2. 2.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 180 cu cm (b) 18 cu cm (c) 216 cu cm (d) 19 cu cm
3. 3.If the radius of a circle 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
4. 4.If the side of a square 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
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
8. 8.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
9. 9.A cuboid is 10 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 22 cu cm (b) 280 cu cm (c) 200 cu cm (d) 20 cu cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
13. 13.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 256 cu cm (d) 384 cu cm
14. 14.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) 16 times (d) 4 times
15. 15.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 54 sq cm (d) 27 sq cm
16. 16.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 24 cu cm (d) 8 cu cm
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
20. 20.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
21. 21.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 164 sq cm (b) 82 sq cm (c) 41 sq cm (d) 42 sq cm
22. 22.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 9 cu cm (c) 10 cu cm (d) 48 cu cm
23. 23.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
24. 24.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
25. 25.A cuboid is 12 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 318 sq cm (b) 1080 sq cm (c) 636 sq cm (d) 1272 sq cm
26. 26.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
29. 29.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
30. 30.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) 64 times (c) 4 times (d) 8 times
31. 31.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 124 cu cm (b) 72 cu cm (c) 15 cu cm (d) 8 cu cm
32. 32.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 472 sq cm (b) 236 sq cm (c) 118 sq cm (d) 240 sq cm
33. 33.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 172 sq cm (b) 344 sq cm (c) 112 sq cm (d) 86 sq cm
34. 34.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
35. 35.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
36. 36.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 36 cu cm (d) 1728 cu cm
37. 37.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) 3 times (d) 6 times
38. 38.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
39. 39.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm
40. 40.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm

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