Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 675 · 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 diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
3. 3.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) 6 times (d) 27 times
4. 4.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) 8 times (d) 2 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) 125 times (b) 25 times (c) 10 times (d) 5 times
6. 6.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 729 sq cm (d) 81 sq cm
7. 7.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
8. 8.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) 6 times (d) 4 times
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
10. 10.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
11. 11.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 126 cu cm (b) 63 cu cm (c) 190 cu cm (d) 18 cu cm
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
13. 13.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 64 cu cm (d) 96 cu cm
14. 14.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
15. 15.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
16. 16.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
17. 17.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 9 cu cm (b) 52 cu cm (c) 8 cu cm (d) 24 cu cm
18. 18.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 144 sq cm (d) 216 sq cm
19. 19.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
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
21. 21.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
23. 23.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
24. 24.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
26. 26.A cuboid is 11 cm long, 10 cm wide and 4 cm high. What is its total surface area? (a) 194 sq cm (b) 440 sq cm (c) 776 sq cm (d) 388 sq cm
27. 27.A cuboid is 9 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 324 cu cm (b) 22 cu cm (c) 306 cu cm (d) 36 cu cm
28. 28.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
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
30. 30.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 49 sq cm (d) 343 sq cm
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
32. 32.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
33. 33.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 400 cu cm (c) 30 cu cm (d) 600 cu cm
34. 34.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 64 sq cm (c) 384 sq cm (d) 256 sq cm
35. 35.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
36. 36.A cuboid is 11 cm long, 9 cm wide and 9 cm high. What is its volume? (a) 558 cu cm (b) 29 cu cm (c) 99 cu cm (d) 891 cu cm
37. 37.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 66 cu cm (b) 10 cu cm (c) 12 cu cm (d) 36 cu cm
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
39. 39.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 104 sq cm (c) 52 sq cm (d) 26 sq cm
40. 40.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

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