Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 234 · 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 diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
2. 2.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
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
4. 4.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 160 sq cm (b) 80 sq cm (c) 40 sq cm (d) 36 sq cm
5. 5.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
6. 6.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 54 sq cm (d) 9 sq cm
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
8. 8.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
9. 9.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
10. 10.A cuboid is 12 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 720 sq cm (b) 504 sq cm (c) 1008 sq cm (d) 252 sq cm
11. 11.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
14. 14.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
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
16. 16.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
17. 17.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 30 cu cm (b) 60 cu cm (c) 13 cu cm (d) 104 cu cm
18. 18.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
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
21. 21.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
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
25. 25.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
26. 26.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
27. 27.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
28. 28.A cuboid is 11 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 167 sq cm (b) 334 sq cm (c) 668 sq cm (d) 385 sq cm
29. 29.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
30. 30.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) 27 times (c) 6 times (d) 3 times
31. 31.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
32. 32.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
33. 33.A cuboid is 7 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 94 sq cm (b) 168 sq cm (c) 376 sq cm (d) 188 sq cm
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
35. 35.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
36. 36.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) 10 times (c) 5 times (d) 125 times
37. 37.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
38. 38.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
39. 39.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 144 sq cm
40. 40.A cuboid is 11 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 26 cu cm (b) 438 cu cm (c) 66 cu cm (d) 594 cu cm

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