Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 158 · 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 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
3. 3.A cuboid is 10 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 134 sq cm (b) 536 sq cm (c) 268 sq cm (d) 240 sq cm
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
5. 5.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
6. 6.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) 16 times (c) 64 times (d) 8 times
7. 7.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
9. 9.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) 2 times (c) 5 times (d) 4 times
10. 10.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
12. 12.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) 64 times (d) 16 times
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
15. 15.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
16. 16.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
19. 19.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) 27 times (d) 6 times
20. 20.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 189 sq cm (b) 222 sq cm (c) 111 sq cm (d) 444 sq cm
21. 21.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 4 sq cm (d) 24 sq cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
23. 23.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 600 sq cm (c) 400 sq cm (d) 100 sq cm
24. 24.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) 64 times (c) 16 times (d) 8 times
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
28. 28.A cuboid is 11 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 388 sq cm (b) 194 sq cm (c) 776 sq cm (d) 440 sq cm
29. 29.A cuboid is 7 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 147 sq cm (b) 91 sq cm (c) 182 sq cm (d) 364 sq cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
31. 31.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 174 sq cm (b) 135 sq cm (c) 348 sq cm (d) 87 sq cm
32. 32.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 64 cu cm (d) 96 cu cm
33. 33.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
34. 34.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
35. 35.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
36. 36.A cuboid is 10 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 138 sq cm (b) 69 sq cm (c) 276 sq cm (d) 90 sq cm
37. 37.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 24 cu cm (d) 16 cu cm
38. 38.A cuboid is 7 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 484 sq cm (b) 210 sq cm (c) 242 sq cm (d) 121 sq cm
39. 39.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) 25 times (d) 10 times
40. 40.A cuboid is 8 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 21 cu cm (b) 48 cu cm (c) 336 cu cm (d) 292 cu cm

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