Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 104 · 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 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 6 times (d) 8 times
2. 2.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
3. 3.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 27 cu cm (d) 324 cu cm
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
5. 5.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) 5 times (c) 4 times (d) 2 times
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
7. 7.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) 125 times (d) 25 times
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
9. 9.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
11. 11.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
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
14. 14.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) 125 times (c) 25 times (d) 5 times
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
17. 17.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 486 sq cm (d) 81 sq cm
18. 18.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
19. 19.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
20. 20.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 172 sq cm (b) 112 sq cm (c) 344 sq cm (d) 86 sq cm
21. 21.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
22. 22.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) 5 times (c) 125 times (d) 10 times
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
27. 27.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 24 cu cm (b) 144 cu cm (c) 17 cu cm (d) 180 cu cm
28. 28.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
30. 30.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
31. 31.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 4 sq cm (c) 8 sq cm (d) 16 sq cm
32. 32.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 162 sq cm (b) 126 sq cm (c) 324 sq cm (d) 81 sq cm
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
34. 34.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 24 sq cm (b) 52 sq cm (c) 104 sq cm (d) 26 sq cm
35. 35.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) 27 times (d) 6 times
36. 36.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 56 cu cm (b) 12 cu cm (c) 10 cu cm (d) 24 cu cm
37. 37.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
38. 38.A cuboid is 9 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 17 cu cm (b) 168 cu cm (c) 18 cu cm (d) 108 cu cm
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
40. 40.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 144 sq cm (d) 217 sq cm

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