Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 644 · 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 radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
3. 3.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 6 times (d) 8 times
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
5. 5.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 440 sq cm (b) 110 sq cm (c) 220 sq cm (d) 200 sq cm
6. 6.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) 10 times (c) 125 times (d) 25 times
7. 7.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 36 cu cm (d) 1728 cu cm
8. 8.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 864 sq cm
9. 9.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
10. 10.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 252 sq cm (b) 63 sq cm (c) 90 sq cm (d) 126 sq cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
12. 12.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 484 sq cm (d) 1331 sq cm
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
15. 15.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) 84 sq cm (d) 18 sq cm
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
18. 18.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) 5 times (c) 10 times (d) 125 times
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 8 sq cm (d) 24 sq cm
20. 20.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 60 sq cm (b) 47 sq cm (c) 188 sq cm (d) 94 sq cm
21. 21.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 486 sq cm (d) 324 sq cm
22. 22.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
23. 23.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) 5 times (c) 125 times (d) 10 times
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
25. 25.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) 9 times (d) 6 times
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
27. 27.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 122 cu cm (b) 12 cu cm (c) 14 cu cm (d) 84 cu cm
28. 28.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 729 cu cm (d) 27 cu cm
29. 29.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
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
31. 31.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 31 sq cm (b) 124 sq cm (c) 62 sq cm (d) 30 sq cm
32. 32.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 33 cu cm
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
34. 34.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 81 cu cm (c) 27 cu cm (d) 126 cu cm
35. 35.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
36. 36.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 512 cu cm (c) 256 cu cm (d) 24 cu cm
37. 37.A cuboid is 11 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 61 sq cm (b) 244 sq cm (c) 66 sq cm (d) 122 sq cm
38. 38.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
39. 39.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 36 sq cm (d) 27 sq cm
40. 40.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm

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