Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 747 · 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 circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
3. 3.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 174 sq cm (b) 348 sq cm (c) 87 sq cm (d) 135 sq cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
5. 5.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
6. 6.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
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
8. 8.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 108 sq cm (b) 150 sq cm (c) 300 sq cm (d) 75 sq cm
9. 9.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
10. 10.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 150 sq cm (d) 100 sq cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
12. 12.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) 6 times (c) 27 times (d) 3 times
13. 13.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
14. 14.A cuboid is 7 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 28 cu cm (b) 112 cu cm (c) 144 cu cm (d) 15 cu cm
15. 15.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
16. 16.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 196 cu cm (d) 294 cu cm
17. 17.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
18. 18.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) 27 times (c) 6 times (d) 9 times
19. 19.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
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
21. 21.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
22. 22.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
23. 23.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
24. 24.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm
25. 25.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 54 sq cm (b) 102 sq cm (c) 204 sq cm (d) 51 sq cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
27. 27.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
28. 28.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm
29. 29.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 217 sq cm (d) 144 sq cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 2 times (d) 8 times
31. 31.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) 5 times (d) 25 times
32. 32.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) 4 times (c) 64 times (d) 8 times
33. 33.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 8 cu cm (b) 88 cu cm (c) 48 cu cm (d) 12 cu cm
34. 34.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 42 cu cm (c) 82 cu cm (d) 12 cu cm
35. 35.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
36. 36.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 16 sq cm (d) 97 sq cm
37. 37.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
38. 38.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 160 cu cm (b) 96 cu cm (c) 18 cu cm (d) 48 cu cm
39. 39.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
40. 40.A cuboid is 8 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 46 sq cm (b) 48 sq cm (c) 92 sq cm (d) 184 sq cm

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