Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 348 · 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 surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
2. 2.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) 4 times (c) 2 times (d) 8 times
3. 3.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 294 sq cm (d) 49 sq cm
4. 4.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 726 sq cm
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
8. 8.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) 4 times (c) 2 times (d) 8 times
9. 9.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) 25 times (c) 125 times (d) 5 times
10. 10.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 864 sq cm (d) 1728 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 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) 3 times (b) 27 times (c) 6 times (d) 9 times
16. 16.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
17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
18. 18.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 6 cu cm (d) 8 cu cm
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
20. 20.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
21. 21.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
22. 22.A cuboid is 12 cm long, 11 cm wide and 7 cm high. What is its volume? (a) 30 cu cm (b) 924 cu cm (c) 132 cu cm (d) 586 cu cm
23. 23.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
24. 24.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) 4 times (c) 2 times (d) 5 times
25. 25.If the radius of a circle 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
26. 26.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 100 sq cm (c) 400 sq cm (d) 600 sq cm
27. 27.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 12 cu cm (d) 64 cu cm
28. 28.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
30. 30.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 108 cu cm (c) 13 cu cm (d) 72 cu cm
31. 31.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
32. 32.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
33. 33.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 88 sq cm (b) 176 sq cm (c) 48 sq cm (d) 44 sq cm
34. 34.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
35. 35.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 144 sq cm (d) 36 sq cm
36. 36.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 64 sq cm (d) 384 sq cm
37. 37.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 11 cu cm (c) 36 cu cm (d) 72 cu cm
38. 38.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) 6 times (d) 9 times
39. 39.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) 3 times (c) 9 times (d) 27 times
40. 40.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

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