Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 574 · 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 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
4. 4.A cuboid is 12 cm long, 10 cm wide and 6 cm high. What is its total surface area? (a) 720 sq cm (b) 252 sq cm (c) 504 sq cm (d) 1008 sq cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
6. 6.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
7. 7.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) 2 times (c) 8 times (d) 4 times
8. 8.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
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
10. 10.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
13. 13.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
14. 14.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 144 sq cm (b) 424 sq cm (c) 212 sq cm (d) 106 sq cm
15. 15.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 82 sq cm (b) 41 sq cm (c) 42 sq cm (d) 164 sq cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
17. 17.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
18. 18.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 50 sq cm (b) 90 sq cm (c) 180 sq cm (d) 45 sq cm
19. 19.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 30 cu cm (d) 400 cu cm
20. 20.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 30 sq cm (d) 31 sq cm
21. 21.A cuboid is 7 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 126 sq cm (b) 324 sq cm (c) 81 sq cm (d) 162 sq cm
22. 22.A cuboid is 12 cm long, 11 cm wide and 10 cm high. What is its total surface area? (a) 362 sq cm (b) 724 sq cm (c) 1320 sq cm (d) 1448 sq cm
23. 23.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
24. 24.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
25. 25.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 112 sq cm (b) 224 sq cm (c) 56 sq cm (d) 60 sq cm
26. 26.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 400 sq cm
27. 27.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
30. 30.A cuboid is 11 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 240 sq cm (b) 704 sq cm (c) 960 sq cm (d) 480 sq cm
31. 31.A cuboid is 11 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 504 sq cm (b) 126 sq cm (c) 252 sq cm (d) 176 sq cm
32. 32.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
33. 33.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
34. 34.If the radius of a circle 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
35. 35.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 94 cu cm (b) 12 cu cm (c) 61 cu cm (d) 60 cu cm
36. 36.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
37. 37.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
38. 38.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times

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