Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 184 · 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) 25 times (c) 125 times (d) 10 times
2. 2.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) 8 times (d) 64 times
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
6. 6.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 6 cu cm (b) 62 cu cm (c) 10 cu cm (d) 30 cu cm
7. 7.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 216 sq cm (d) 144 sq cm
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
9. 9.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) 8 times (c) 4 times (d) 5 times
10. 10.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
11. 11.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
12. 12.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 146 sq cm (b) 292 sq cm (c) 90 sq cm (d) 73 sq cm
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
14. 14.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
15. 15.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
16. 16.A cuboid is 12 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 48 cu cm (b) 23 cu cm (c) 336 cu cm (d) 320 cu cm
17. 17.What is the area of a circle of radius 7 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 area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
21. 21.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 27 sq cm (d) 36 sq cm
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
23. 23.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
24. 24.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
25. 25.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
27. 27.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 30 cu cm (d) 1000 cu cm
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
29. 29.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
31. 31.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
32. 32.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 8 cu cm (c) 17 cu cm (d) 16 cu cm
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
34. 34.A cuboid is 12 cm long, 10 cm wide and 7 cm high. What is its total surface area? (a) 840 sq cm (b) 1096 sq cm (c) 274 sq cm (d) 548 sq cm
35. 35.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 21 cu cm (d) 343 cu cm
36. 36.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) 25 times (c) 10 times (d) 125 times
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
38. 38.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 9 cu cm (d) 54 cu cm
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
40. 40.A cuboid is 7 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 162 sq cm (d) 126 sq cm

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