Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 551 · 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 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 4 times (d) 2 times
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
3. 3.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
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
5. 5.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
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
7. 7.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) 16 times (c) 4 times (d) 8 times
8. 8.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) 5 times (c) 8 times (d) 4 times
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
10. 10.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 90 sq cm (b) 54 sq cm (c) 180 sq cm (d) 45 sq cm
11. 11.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) 6 times (c) 9 times (d) 27 times
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
14. 14.A cuboid is 12 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 288 sq cm (b) 624 sq cm (c) 156 sq cm (d) 312 sq cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
16. 16.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 138 sq cm (b) 280 sq cm (c) 276 sq cm (d) 552 sq cm
17. 17.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
18. 18.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 6 cu cm (d) 16 cu cm
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
20. 20.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
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
23. 23.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 59 sq cm (b) 70 sq cm (c) 236 sq cm (d) 118 sq cm
24. 24.A cuboid is 9 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 135 sq cm (b) 174 sq cm (c) 87 sq cm (d) 348 sq cm
25. 25.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) 9 times (c) 3 times (d) 6 times
26. 26.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 600 sq cm (d) 100 sq cm
27. 27.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 16 cu cm (b) 126 cu cm (c) 162 cu cm (d) 18 cu cm
28. 28.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 121 sq cm (d) 484 sq cm
29. 29.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 716 sq cm (b) 358 sq cm (c) 396 sq cm (d) 179 sq cm
30. 30.A cuboid is 11 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 792 cu cm (b) 518 cu cm (c) 28 cu cm (d) 99 cu cm
31. 31.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 190 cu cm (b) 15 cu cm (c) 18 cu cm (d) 150 cu cm
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
33. 33.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) 2 times (c) 4 times (d) 8 times
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
35. 35.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 243 cu cm (b) 21 cu cm (c) 270 cu cm (d) 27 cu cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 52 cu cm (b) 12 cu cm (c) 9 cu cm (d) 24 cu cm
37. 37.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
38. 38.A cuboid is 9 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 51 sq cm (b) 204 sq cm (c) 102 sq cm (d) 54 sq cm
39. 39.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm

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