Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 135 · 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.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 6 cu cm (d) 24 cu cm
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
3. 3.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 64 cu cm (d) 65 cu cm
4. 4.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
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
7. 7.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 54 sq cm (d) 36 sq cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
9. 9.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) 125 times (d) 5 times
10. 10.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) 64 times (c) 8 times (d) 16 times
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
12. 12.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) 3 times (c) 27 times (d) 9 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.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 384 cu cm (d) 24 cu cm
15. 15.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
16. 16.A cuboid is 11 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 23 cu cm (b) 55 cu cm (c) 385 cu cm (d) 334 cu cm
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
18. 18.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 96 sq cm (d) 64 sq cm
19. 19.A cuboid is 9 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 117 sq cm (b) 468 sq cm (c) 234 sq cm (d) 162 sq cm
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
21. 21.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 168 cu cm (b) 17 cu cm (c) 24 cu cm (d) 188 cu cm
22. 22.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 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) 5 times (b) 10 times (c) 125 times (d) 25 times
24. 24.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 8 cu cm (d) 18 cu cm
25. 25.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 486 cu cm (d) 729 cu cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
28. 28.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
29. 29.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
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 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 9 cu cm (d) 54 cu cm
32. 32.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 864 cu cm (d) 1728 cu cm
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
34. 34.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 164 cu cm (b) 17 cu cm (c) 30 cu cm (d) 120 cu cm
35. 35.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 25 sq cm (d) 125 sq cm
36. 36.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
37. 37.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) 64 times (d) 8 times
38. 38.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
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
40. 40.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

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