Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 412 · 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.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
3. 3.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 16 cu cm (d) 8 cu cm
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
7. 7.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
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
10. 10.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 36 sq cm (d) 27 sq cm
11. 11.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
12. 12.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 100 sq cm (d) 1000 sq cm
13. 13.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 124 sq cm (b) 30 sq cm (c) 31 sq cm (d) 62 sq cm
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
15. 15.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 100 sq cm (c) 150 sq cm (d) 25 sq cm
16. 16.A cuboid is 10 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 440 cu cm (b) 600 cu cm (c) 26 cu cm (d) 60 cu cm
17. 17.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
18. 18.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 13 cu cm (b) 10 cu cm (c) 60 cu cm (d) 104 cu cm
19. 19.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
21. 21.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) 8 times (c) 16 times (d) 64 times
22. 22.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
23. 23.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 4 sq cm (d) 8 sq cm
24. 24.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 14 cu cm (b) 21 cu cm (c) 122 cu cm (d) 84 cu cm
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
26. 26.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) 4 times (c) 8 times (d) 2 times
27. 27.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
28. 28.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 90 sq cm (b) 144 sq cm (c) 360 sq cm (d) 180 sq cm
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
31. 31.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 97 sq cm (d) 16 sq cm
32. 32.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
33. 33.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 36 cu cm (b) 11 cu cm (c) 6 cu cm (d) 72 cu cm
36. 36.A cuboid is 12 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 320 cu cm (b) 336 cu cm (c) 84 cu cm (d) 23 cu cm
37. 37.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) 5 times (d) 125 times
38. 38.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) 4 times (c) 8 times (d) 16 times
39. 39.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 160 sq cm (b) 80 sq cm (c) 100 sq cm (d) 320 sq cm
40. 40.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm

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