Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 527 · 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 side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
3. 3.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) 64 times (c) 16 times (d) 8 times
4. 4.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
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
7. 7.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) 16 times (d) 64 times
8. 8.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
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
12. 12.A cuboid is 8 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 19 cu cm (b) 224 cu cm (c) 232 cu cm (d) 32 cu cm
13. 13.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 30 cu cm (b) 126 cu cm (c) 14 cu cm (d) 90 cu cm
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
15. 15.A cuboid is 12 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 672 sq cm (b) 944 sq cm (c) 236 sq cm (d) 472 sq cm
16. 16.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
18. 18.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
19. 19.A cuboid is 11 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 221 sq cm (b) 616 sq cm (c) 884 sq cm (d) 442 sq cm
20. 20.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm
21. 21.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
22. 22.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 94 sq cm (b) 60 sq cm (c) 188 sq cm (d) 47 sq cm
23. 23.A cuboid is 8 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 210 cu cm (b) 200 cu cm (c) 18 cu cm (d) 40 cu cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
25. 25.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
26. 26.A cuboid is 12 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 244 cu cm (b) 24 cu cm (c) 21 cu cm (d) 168 cu cm
27. 27.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
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
29. 29.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
31. 31.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) 4 times (c) 5 times (d) 2 times
32. 32.A cuboid is 9 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 222 cu cm (b) 63 cu cm (c) 19 cu cm (d) 189 cu cm
33. 33.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 150 sq cm (d) 125 sq cm
34. 34.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) 5 times (c) 25 times (d) 10 times
35. 35.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 100 sq cm
36. 36.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
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
38. 38.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 27 cu cm (c) 729 cu cm (d) 486 cu cm
39. 39.A cuboid is 11 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 17 cu cm (b) 148 cu cm (c) 22 cu cm (d) 88 cu cm
40. 40.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm

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