Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 41 · 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.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
4. 4.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
5. 5.A cuboid is 9 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 336 sq cm (b) 168 sq cm (c) 108 sq cm (d) 84 sq cm
6. 6.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
7. 7.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
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
10. 10.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
11. 11.A cuboid is 8 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 184 cu cm (b) 160 cu cm (c) 32 cu cm (d) 17 cu cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
13. 13.A cuboid is 8 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 208 cu cm (b) 192 cu cm (c) 32 cu cm (d) 18 cu cm
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
15. 15.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 384 cu cm (d) 512 cu cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
17. 17.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
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
19. 19.A cuboid is 11 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 88 cu cm (b) 44 cu cm (c) 148 cu cm (d) 17 cu cm
20. 20.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
21. 21.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
22. 22.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
23. 23.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) 9 times (c) 3 times (d) 6 times
24. 24.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
25. 25.A cuboid is 6 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 72 cu cm (b) 13 cu cm (c) 108 cu cm (d) 18 cu cm
26. 26.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 32 sq cm (c) 64 sq cm (d) 12 sq cm
27. 27.A cuboid is 8 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 40 cu cm (b) 288 cu cm (c) 21 cu cm (d) 320 cu cm
28. 28.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) 9 times (d) 27 times
29. 29.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) 5 times (c) 25 times (d) 125 times
30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
32. 32.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 36 cu cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 6 cu cm (b) 9 cu cm (c) 52 cu cm (d) 24 cu cm
34. 34.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) 2 times (c) 8 times (d) 5 times
35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
36. 36.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
37. 37.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
38. 38.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) 27 times (c) 3 times (d) 9 times
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
40. 40.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) 64 times (c) 16 times (d) 4 times

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