Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 38 · 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 radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
2. 2.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
4. 4.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
5. 5.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 254 cu cm (b) 20 cu cm (c) 252 cu cm (d) 63 cu cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
7. 7.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
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
9. 9.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 13 cu cm (c) 72 cu cm (d) 108 cu cm
10. 10.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
11. 11.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 44 sq cm (b) 176 sq cm (c) 48 sq cm (d) 88 sq cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
13. 13.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
14. 14.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
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
17. 17.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm
18. 18.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
20. 20.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) 125 times (c) 25 times (d) 10 times
21. 21.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) 5 times (c) 4 times (d) 8 times
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
23. 23.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 96 sq cm (d) 16 sq cm
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
25. 25.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 36 cu cm (d) 576 cu cm
26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
27. 27.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
28. 28.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
29. 29.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
30. 30.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 125 cu cm (d) 100 cu cm
31. 31.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 9 cu cm (d) 36 cu cm
32. 32.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 82 sq cm (b) 164 sq cm (c) 41 sq cm (d) 42 sq cm
33. 33.A cuboid is 12 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 180 cu cm (c) 60 cu cm (d) 222 cu cm
34. 34.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 36 sq cm (d) 54 sq cm
35. 35.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 62 cu cm (b) 30 cu cm (c) 10 cu cm (d) 31 cu cm
36. 36.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) 2 times (c) 4 times (d) 6 times
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
38. 38.A cuboid is 11 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 396 sq cm (b) 179 sq cm (c) 716 sq cm (d) 358 sq cm
39. 39.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
40. 40.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 248 sq cm (b) 62 sq cm (c) 72 sq cm (d) 124 sq cm

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