Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 723 · 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 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
3. 3.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
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
5. 5.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) 25 times (c) 125 times (d) 10 times
6. 6.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) 25 times (c) 10 times (d) 5 times
7. 7.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
8. 8.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
9. 9.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
10. 10.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 21 cu cm (d) 196 cu cm
11. 11.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) 6 times (c) 27 times (d) 9 times
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
14. 14.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
17. 17.A cuboid is 10 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 560 sq cm (b) 280 sq cm (c) 140 sq cm (d) 200 sq cm
18. 18.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 30 sq cm (d) 31 sq cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 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) 2 times (b) 8 times (c) 4 times (d) 5 times
22. 22.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
23. 23.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
24. 24.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
25. 25.A cuboid is 12 cm long, 7 cm wide and 6 cm high. What is its volume? (a) 25 cu cm (b) 84 cu cm (c) 396 cu cm (d) 504 cu cm
26. 26.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 80 sq cm (b) 20 sq cm (c) 40 sq cm (d) 16 sq cm
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
28. 28.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 100 cu cm (b) 13 cu cm (c) 56 cu cm (d) 8 cu cm
29. 29.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 248 sq cm (b) 240 sq cm (c) 496 sq cm (d) 124 sq cm
30. 30.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) 9 times (c) 27 times (d) 3 times
31. 31.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
32. 32.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
34. 34.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 54 cu cm (c) 27 cu cm (d) 9 cu cm
35. 35.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) 3 times (c) 6 times (d) 9 times
36. 36.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 500 sq cm (b) 400 sq cm (c) 800 sq cm (d) 200 sq cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 82 sq cm (c) 164 sq cm (d) 42 sq cm
38. 38.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
39. 39.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times

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