Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 226 · 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) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
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) 10 times (c) 125 times (d) 5 times
5. 5.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
6. 6.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 16 cu cm (d) 6 cu cm
7. 7.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
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
9. 9.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
10. 10.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
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
12. 12.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 4 sq cm (d) 16 sq cm
13. 13.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
15. 15.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
16. 16.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 125 cu cm (d) 150 cu cm
17. 17.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
21. 21.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 216 sq cm (d) 217 sq cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
23. 23.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
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
25. 25.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 1331 sq cm (d) 726 sq cm
26. 26.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
27. 27.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 127 sq cm (b) 254 sq cm (c) 508 sq cm (d) 252 sq cm
28. 28.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 49 sq cm (d) 294 sq cm
29. 29.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 729 sq cm (d) 81 sq cm
30. 30.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
31. 31.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) 2 times (c) 5 times (d) 4 times
32. 32.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
33. 33.A cuboid is 12 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 141 sq cm (b) 252 sq cm (c) 282 sq cm (d) 564 sq cm
34. 34.A cuboid is 9 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 360 sq cm (b) 166 sq cm (c) 664 sq cm (d) 332 sq cm
35. 35.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 16 cu cm (b) 17 cu cm (c) 112 cu cm (d) 172 cu cm
36. 36.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
37. 37.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 484 cu cm (d) 33 cu cm
38. 38.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
40. 40.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) 4 times (c) 8 times (d) 5 times

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