Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 101 · 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 radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
2. 2.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
5. 5.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 90 sq cm (b) 73 sq cm (c) 292 sq cm (d) 146 sq cm
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
7. 7.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
8. 8.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 31 sq cm (d) 30 sq 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) 5 times (b) 125 times (c) 10 times (d) 25 times
12. 12.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
13. 13.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 36 sq cm (b) 33 sq cm (c) 66 sq cm (d) 132 sq cm
14. 14.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
15. 15.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
16. 16.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
17. 17.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
20. 20.A cuboid is 6 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 13 cu cm (b) 18 cu cm (c) 108 cu cm (d) 72 cu cm
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
22. 22.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 125 cu cm (d) 15 cu cm
23. 23.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
25. 25.A cuboid is 10 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 450 sq cm (b) 185 sq cm (c) 740 sq cm (d) 370 sq cm
26. 26.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
27. 27.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 576 cu cm (d) 864 cu cm
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
30. 30.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 248 sq cm (b) 62 sq cm (c) 72 sq cm (d) 124 sq cm
31. 31.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 272 sq cm (b) 96 sq cm (c) 68 sq cm (d) 136 sq cm
32. 32.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 94 cu cm (c) 20 cu cm (d) 60 cu cm
33. 33.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 256 sq cm (d) 512 sq cm
34. 34.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) 8 times (c) 6 times (d) 4 times
35. 35.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
37. 37.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) 9 times (c) 6 times (d) 3 times
38. 38.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 80 sq cm (b) 40 sq cm (c) 160 sq cm (d) 48 sq cm
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
40. 40.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times

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