Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 69 · 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 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
2. 2.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
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
5. 5.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) 5 times (c) 10 times (d) 125 times
6. 6.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) 125 times (d) 5 times
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
8. 8.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
9. 9.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
10. 10.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
13. 13.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) 25 times (d) 10 times
14. 14.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 52 sq cm (b) 24 sq cm (c) 104 sq cm (d) 26 sq cm
15. 15.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) 2 times (d) 8 times
16. 16.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
17. 17.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
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
19. 19.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) 5 times (d) 8 times
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
21. 21.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 54 sq cm (d) 36 sq cm
22. 22.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 384 sq cm (d) 512 sq cm
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
24. 24.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
25. 25.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) 27 times (d) 9 times
26. 26.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 90 sq cm (b) 252 sq cm (c) 63 sq cm (d) 126 sq cm
27. 27.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
28. 28.A cuboid is 12 cm long, 8 cm wide and 3 cm high. What is its volume? (a) 312 cu cm (b) 96 cu cm (c) 288 cu cm (d) 23 cu cm
29. 29.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) 16 times (d) 64 times
30. 30.A cuboid is 12 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 648 sq cm (b) 936 sq cm (c) 468 sq cm (d) 234 sq cm
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 26 sq cm (b) 52 sq cm (c) 104 sq cm (d) 24 sq cm
34. 34.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 176 sq cm (b) 88 sq cm (c) 44 sq cm (d) 48 sq cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 82 sq cm (c) 164 sq cm (d) 42 sq cm
36. 36.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
37. 37.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 729 sq cm (d) 486 sq cm
38. 38.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 65 cu cm (d) 12 cu cm
39. 39.A cuboid is 8 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 48 cu cm (b) 288 cu cm (c) 20 cu cm (d) 264 cu cm
40. 40.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 12 cu cm (c) 94 cu cm (d) 60 cu cm

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