Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 8 · 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.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
2. 2.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
3. 3.A cuboid is 7 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 70 cu cm (b) 118 cu cm (c) 14 cu cm (d) 71 cu cm
4. 4.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) 3 times (c) 6 times (d) 27 times
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
7. 7.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
8. 8.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 82 sq cm (b) 42 sq cm (c) 164 sq cm (d) 41 sq cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
11. 11.A cuboid is 8 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 752 sq cm (b) 480 sq cm (c) 376 sq cm (d) 188 sq cm
12. 12.A cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 15 cu cm (b) 105 cu cm (c) 142 cu cm (d) 106 cu cm
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
14. 14.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
15. 15.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
16. 16.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
17. 17.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
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
19. 19.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 180 cu cm (d) 17 cu cm
20. 20.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 100 sq cm
21. 21.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 24 cu cm (b) 40 cu cm (c) 360 cu cm (d) 400 cu cm
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
23. 23.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
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
25. 25.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) 5 times (c) 10 times (d) 25 times
26. 26.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
27. 27.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
28. 28.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
29. 29.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
31. 31.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) 4 times (c) 5 times (d) 2 times
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
33. 33.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 56 cu cm (b) 100 cu cm (c) 13 cu cm (d) 8 cu cm
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
35. 35.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 9 cu cm (d) 54 cu cm
36. 36.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 24 cu cm (d) 512 cu cm
37. 37.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 96 sq cm (b) 272 sq cm (c) 136 sq cm (d) 68 sq cm
38. 38.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm

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