Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 886 · 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 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
2. 2.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) 64 times (c) 4 times (d) 16 times
3. 3.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
7. 7.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
8. 8.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
12. 12.A cuboid is 7 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 98 sq cm (b) 77 sq cm (c) 154 sq cm (d) 308 sq cm
13. 13.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 9 sq cm (d) 36 sq cm
14. 14.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
15. 15.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
16. 16.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
17. 17.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 16 sq cm (d) 8 sq cm
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
19. 19.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
20. 20.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
21. 21.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
23. 23.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) 25 times (c) 125 times (d) 10 times
24. 24.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) 4 times (c) 8 times (d) 6 times
25. 25.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 126 sq cm (b) 81 sq cm (c) 324 sq cm (d) 162 sq cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
27. 27.A cuboid is 12 cm long, 8 cm wide and 3 cm high. What is its volume? (a) 23 cu cm (b) 288 cu cm (c) 312 cu cm (d) 96 cu cm
28. 28.A cuboid is 11 cm long, 10 cm wide and 3 cm high. What is its total surface area? (a) 173 sq cm (b) 346 sq cm (c) 692 sq cm (d) 330 sq cm
29. 29.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 121 sq cm (d) 726 sq cm
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
31. 31.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 600 cu cm (d) 1000 cu cm
32. 32.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
33. 33.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 108 sq cm (b) 180 sq cm (c) 216 sq cm (d) 432 sq cm
34. 34.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
35. 35.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 9 cu cm (d) 36 cu cm
36. 36.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 126 cu cm (c) 30 cu cm (d) 90 cu cm
37. 37.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
38. 38.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 84 cu cm (b) 14 cu cm (c) 15 cu cm (d) 136 cu cm
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
40. 40.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) 8 times (c) 4 times (d) 16 times

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