Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 698 · 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 the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
5. 5.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
7. 7.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
8. 8.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) 16 times (c) 4 times (d) 64 times
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
13. 13.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 8 sq cm (d) 16 sq cm
14. 14.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 600 cu cm (d) 1000 cu cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
16. 16.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
17. 17.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
18. 18.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) 2 times (c) 5 times (d) 4 times
19. 19.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 576 cu cm (c) 36 cu cm (d) 864 cu cm
20. 20.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
21. 21.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
22. 22.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 30 sq cm (c) 31 sq cm (d) 62 sq cm
23. 23.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
24. 24.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
25. 25.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
26. 26.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) 16 times (c) 8 times (d) 4 times
27. 27.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
28. 28.A cuboid is 8 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 32 cu cm (b) 184 cu cm (c) 160 cu cm (d) 17 cu cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 18 sq cm (c) 21 sq cm (d) 42 sq cm
30. 30.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
31. 31.A cuboid is 9 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 191 sq cm (b) 504 sq cm (c) 382 sq cm (d) 764 sq cm
32. 32.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) 9 times (c) 3 times (d) 27 times
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
34. 34.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
35. 35.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
36. 36.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 9 cu cm (d) 54 cu cm
37. 37.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 360 sq cm (b) 180 sq cm (c) 400 sq cm (d) 720 sq cm
38. 38.A cuboid is 3 cm long, 2 cm wide and 9 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.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
40. 40.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm

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