Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 119 · 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 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
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
4. 4.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) 8 times (d) 4 times
5. 5.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 166 sq cm (b) 360 sq cm (c) 332 sq cm (d) 664 sq cm
6. 6.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
7. 7.A cuboid is 7 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 280 sq cm (b) 262 sq cm (c) 131 sq cm (d) 524 sq cm
8. 8.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
9. 9.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 864 sq cm (c) 576 sq cm (d) 144 sq cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
11. 11.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) 125 times (d) 10 times
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
13. 13.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
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
15. 15.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
16. 16.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) 9 times (d) 3 times
17. 17.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
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
19. 19.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 10 cu cm (b) 146 cu cm (c) 90 cu cm (d) 16 cu cm
20. 20.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
21. 21.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
22. 22.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) 16 times (c) 4 times (d) 8 times
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) 10 times (c) 125 times (d) 25 times
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
25. 25.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
26. 26.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 42 sq cm (c) 18 sq cm (d) 84 sq cm
27. 27.A cuboid is 10 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 138 sq cm (b) 280 sq cm (c) 552 sq cm (d) 276 sq cm
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
29. 29.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
30. 30.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 12 cu cm (c) 60 cu cm (d) 20 cu cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 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) 3 times (c) 27 times (d) 9 times
33. 33.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) 16 times (c) 4 times (d) 64 times
34. 34.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
35. 35.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 54 sq cm (d) 36 sq cm
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
37. 37.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
38. 38.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 256 cu cm (d) 24 cu cm
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
40. 40.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm

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