Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 853 · 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 diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
2. 2.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
3. 3.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
5. 5.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
6. 6.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 9 cu cm (d) 27 cu cm
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
9. 9.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) 9 times (c) 6 times (d) 27 times
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
11. 11.If the side of a square 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
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
13. 13.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
14. 14.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
15. 15.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
16. 16.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 726 sq cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
18. 18.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 36 sq cm (b) 144 sq cm (c) 72 sq cm (d) 73 sq cm
19. 19.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
20. 20.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) 4 times (c) 8 times (d) 5 times
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
23. 23.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) 3 times (c) 9 times (d) 27 times
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
26. 26.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
27. 27.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) 6 times (c) 3 times (d) 9 times
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
30. 30.A cuboid is 8 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 368 sq cm (b) 160 sq cm (c) 92 sq cm (d) 184 sq cm
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
32. 32.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 66 sq cm (b) 36 sq cm (c) 33 sq cm (d) 132 sq cm
33. 33.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
34. 34.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 720 sq cm (b) 180 sq cm (c) 400 sq cm (d) 360 sq cm
35. 35.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
36. 36.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
37. 37.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 135 sq cm (b) 540 sq cm (c) 270 sq cm (d) 243 sq cm
38. 38.A cuboid is 12 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 720 sq cm (b) 360 sq cm (c) 432 sq cm (d) 180 sq cm
39. 39.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 21 sq cm (c) 84 sq cm (d) 42 sq cm
40. 40.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 40 sq cm (b) 16 sq cm (c) 80 sq cm (d) 20 sq cm

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