Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 81 · 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 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
2. 2.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
3. 3.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq 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) 176 cm (d) 2464 cm
6. 6.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 280 cu cm (b) 21 cu cm (c) 300 cu cm (d) 30 cu cm
7. 7.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
8. 8.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
10. 10.If the side of a square 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
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
13. 13.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
14. 14.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
17. 17.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 27 cu cm (d) 36 cu cm
18. 18.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 125 sq cm (c) 25 sq cm (d) 100 sq cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
20. 20.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) 8 times (d) 6 times
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
22. 22.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 180 sq cm (b) 432 sq cm (c) 108 sq cm (d) 216 sq cm
23. 23.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
25. 25.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) 27 times (c) 9 times (d) 3 times
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 132 cu cm (b) 10 cu cm (c) 15 cu cm (d) 80 cu cm
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
30. 30.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
31. 31.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 136 cu cm (d) 80 cu cm
32. 32.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) 64 times (c) 16 times (d) 4 times
33. 33.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 30 cu cm (b) 10 cu cm (c) 62 cu cm (d) 6 cu cm
34. 34.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
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq 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) 125 times (b) 10 times (c) 5 times (d) 25 times
37. 37.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 512 sq cm (d) 384 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 90 cu cm (b) 10 cu cm (c) 16 cu cm (d) 146 cu cm
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
40. 40.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 600 cu cm

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