Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 967 · 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 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
2. 2.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
3. 3.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
4. 4.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq 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) 8 times (b) 2 times (c) 5 times (d) 4 times
8. 8.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 729 sq cm (d) 324 sq cm
9. 9.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 12 cu cm (d) 82 cu cm
10. 10.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
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
15. 15.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
17. 17.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
18. 18.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) 9 times (c) 27 times (d) 6 times
19. 19.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) 125 times (c) 10 times (d) 5 times
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
21. 21.A cuboid is 8 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 66 sq cm (b) 80 sq cm (c) 132 sq cm (d) 264 sq cm
22. 22.A cuboid is 11 cm long, 10 cm wide and 6 cm high. What is its total surface area? (a) 236 sq cm (b) 660 sq cm (c) 944 sq cm (d) 472 sq cm
23. 23.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 294 cu cm (d) 196 cu cm
24. 24.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 150 sq cm (d) 100 sq cm
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
28. 28.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
29. 29.A cuboid is 9 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 24 cu cm (b) 382 cu cm (c) 72 cu cm (d) 504 cu cm
30. 30.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
31. 31.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
32. 32.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
33. 33.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 60 cu cm (c) 94 cu cm (d) 12 cu cm
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
35. 35.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) 10 times (c) 125 times (d) 5 times
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
37. 37.A cuboid is 12 cm long, 11 cm wide and 7 cm high. What is its total surface area? (a) 1172 sq cm (b) 586 sq cm (c) 924 sq cm (d) 293 sq cm
38. 38.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
39. 39.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 280 cu cm (b) 300 cu cm (c) 30 cu cm (d) 21 cu cm
40. 40.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm

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