Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 116 · 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 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
3. 3.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
4. 4.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
5. 5.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 576 sq cm (d) 864 sq cm
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
7. 7.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
8. 8.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
9. 9.A cuboid is 10 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 688 sq cm (b) 172 sq cm (c) 344 sq cm (d) 420 sq cm
10. 10.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) 8 times (c) 5 times (d) 4 times
11. 11.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 184 sq cm (b) 92 sq cm (c) 46 sq cm (d) 48 sq cm
12. 12.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 60 sq cm (c) 112 sq cm (d) 224 sq cm
13. 13.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
14. 14.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 384 cu cm (d) 24 cu cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
16. 16.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
17. 17.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
18. 18.If the side of a square 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
19. 19.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
20. 20.A cuboid is 11 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 238 sq cm (b) 476 sq cm (c) 220 sq cm (d) 119 sq cm
21. 21.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 217 sq cm (d) 36 sq cm
22. 22.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
23. 23.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
24. 24.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 90 sq cm (b) 126 sq cm (c) 252 sq cm (d) 63 sq cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
26. 26.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
27. 27.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 9 cu cm (d) 36 cu cm
28. 28.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
29. 29.A cuboid is 12 cm long, 9 cm wide and 9 cm high. What is its total surface area? (a) 297 sq cm (b) 1188 sq cm (c) 972 sq cm (d) 594 sq cm
30. 30.A cuboid is 11 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 66 cu cm (b) 122 cu cm (c) 33 cu cm (d) 16 cu cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 32 sq cm (b) 65 sq cm (c) 128 sq cm (d) 64 sq cm
32. 32.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) 27 times (c) 6 times (d) 9 times
33. 33.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 729 sq cm (c) 324 sq cm (d) 81 sq cm
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
35. 35.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) 25 times (c) 5 times (d) 10 times
36. 36.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) 8 times (c) 2 times (d) 4 times
37. 37.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 60 sq cm (b) 188 sq cm (c) 94 sq cm (d) 47 sq cm
38. 38.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
39. 39.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) 4 times (c) 8 times (d) 2 times
40. 40.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) 5 times (c) 125 times (d) 25 times

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