Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 504 · 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 the side of a square 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
2. 2.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
7. 7.A cuboid is 10 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 256 cu cm (b) 21 cu cm (c) 180 cu cm (d) 90 cu cm
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
9. 9.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
10. 10.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) 10 times (c) 25 times (d) 125 times
11. 11.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) 4 times (d) 8 times
12. 12.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
15. 15.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
16. 16.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 188 cu cm (b) 17 cu cm (c) 24 cu cm (d) 168 cu cm
17. 17.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
18. 18.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
19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
20. 20.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
21. 21.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
22. 22.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
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
24. 24.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 24 sq cm (d) 16 sq cm
25. 25.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 11 cu cm (b) 72 cu cm (c) 36 cu cm (d) 6 cu cm
26. 26.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
27. 27.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 24 cu cm (d) 6 cu cm
28. 28.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
29. 29.A cuboid is 9 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 216 sq cm (b) 123 sq cm (c) 492 sq cm (d) 246 sq cm
30. 30.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 24 cu cm (b) 240 cu cm (c) 20 cu cm (d) 248 cu cm
31. 31.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 108 cu cm (c) 13 cu cm (d) 12 cu cm
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
33. 33.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
35. 35.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
36. 36.A cuboid is 11 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 150 cu cm (b) 99 cu cm (c) 17 cu cm (d) 33 cu cm
37. 37.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 9 cu cm (d) 54 cu cm
38. 38.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) 27 times (c) 9 times (d) 3 times
39. 39.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
40. 40.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 16 sq cm (d) 97 sq cm

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