Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 929 · 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 cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 6 cu cm (b) 30 cu cm (c) 10 cu cm (d) 62 cu cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 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.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 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) 125 times (b) 10 times (c) 25 times (d) 5 times
8. 8.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
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
10. 10.A cuboid is 11 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 234 cu cm (b) 20 cu cm (c) 198 cu cm (d) 33 cu cm
11. 11.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
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
13. 13.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 576 sq cm
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
15. 15.A cuboid is 10 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 204 sq cm (b) 408 sq cm (c) 816 sq cm (d) 540 sq cm
16. 16.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 82 cu cm (b) 42 cu cm (c) 12 cu cm (d) 6 cu cm
18. 18.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 54 sq cm (d) 9 sq cm
19. 19.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 121 sq cm (d) 484 sq cm
20. 20.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 400 cu cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 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) 125 times (c) 10 times (d) 5 times
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
24. 24.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
28. 28.A cuboid is 6 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 210 sq cm (b) 428 sq cm (c) 107 sq cm (d) 214 sq cm
29. 29.A cuboid is 7 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 100 cu cm (b) 13 cu cm (c) 28 cu cm (d) 56 cu cm
30. 30.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 168 cu cm (b) 188 cu cm (c) 17 cu cm (d) 42 cu cm
31. 31.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) 64 times (c) 4 times (d) 8 times
32. 32.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
33. 33.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
34. 34.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) 16 times (c) 64 times (d) 8 times
35. 35.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 18 cu cm (c) 54 cu cm (d) 90 cu cm
36. 36.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
37. 37.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) 27 times (d) 6 times
38. 38.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) 10 times (d) 125 times
39. 39.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) 27 times (d) 6 times
40. 40.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm

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