Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 386 · 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 diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
2. 2.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
3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
4. 4.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 104 sq cm (b) 26 sq cm (c) 52 sq cm (d) 24 sq cm
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 100 sq cm (d) 600 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) 9 times (c) 6 times (d) 3 times
7. 7.A cuboid is 11 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 860 sq cm (b) 215 sq cm (c) 550 sq cm (d) 430 sq cm
8. 8.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 384 sq cm (d) 64 sq cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
12. 12.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) 4 times (c) 8 times (d) 2 times
13. 13.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 204 sq cm (b) 54 sq cm (c) 51 sq cm (d) 102 sq cm
14. 14.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 132 cu cm (b) 15 cu cm (c) 10 cu cm (d) 80 cu cm
15. 15.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
16. 16.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) 125 times (c) 25 times (d) 5 times
17. 17.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
18. 18.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
19. 19.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 44 sq cm (b) 88 sq cm (c) 176 sq cm (d) 40 sq cm
20. 20.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 8 cu cm (c) 40 cu cm (d) 16 cu cm
21. 21.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
22. 22.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
23. 23.A cuboid is 12 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 504 cu cm (b) 72 cu cm (c) 28 cu cm (d) 720 cu cm
24. 24.A cuboid is 8 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 228 sq cm (b) 72 sq cm (c) 114 sq cm (d) 57 sq cm
25. 25.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 216 sq cm (d) 144 sq cm
26. 26.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 144 sq cm (b) 180 sq cm (c) 360 sq cm (d) 90 sq cm
27. 27.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
28. 28.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
29. 29.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) 5 times (c) 8 times (d) 4 times
30. 30.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 217 cu cm (d) 144 cu cm
31. 31.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
32. 32.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
33. 33.A cuboid is 8 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 320 cu cm (b) 304 cu cm (c) 32 cu cm (d) 22 cu cm
34. 34.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 81 sq cm (b) 108 sq cm (c) 324 sq cm (d) 162 sq cm
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
36. 36.A cuboid is 11 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 252 sq cm (b) 504 sq cm (c) 176 sq cm (d) 126 sq cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 184 sq cm (b) 48 sq cm (c) 46 sq cm (d) 92 sq cm
38. 38.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
39. 39.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
40. 40.A cuboid is 11 cm long, 10 cm wide and 4 cm high. What is its total surface area? (a) 194 sq cm (b) 388 sq cm (c) 440 sq cm (d) 776 sq cm

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