Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 607 · 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 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
2. 2.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) 5 times (d) 8 times
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
4. 4.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
5. 5.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq cm
6. 6.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 96 sq cm (d) 64 sq cm
7. 7.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 90 sq cm (b) 63 sq cm (c) 252 sq cm (d) 126 sq cm
8. 8.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 36 cu cm
9. 9.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) 25 times (c) 5 times (d) 10 times
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
14. 14.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 294 cu cm (d) 196 cu cm
15. 15.A cuboid is 11 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 33 cu cm (b) 264 cu cm (c) 290 cu cm (d) 22 cu cm
16. 16.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 15 cu cm (b) 148 cu cm (c) 120 cu cm (d) 24 cu cm
17. 17.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
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
19. 19.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
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
21. 21.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
22. 22.If the radius of a circle 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
23. 23.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
24. 24.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
25. 25.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
26. 26.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 sq cm
27. 27.A cuboid is 11 cm long, 8 cm wide and 2 cm high. What is its volume? (a) 88 cu cm (b) 252 cu cm (c) 21 cu cm (d) 176 cu cm
28. 28.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 30 sq cm (b) 62 sq cm (c) 31 sq cm (d) 124 sq cm
29. 29.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
30. 30.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
32. 32.A cuboid is 8 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 40 cu cm (b) 22 cu cm (c) 360 cu cm (d) 314 cu cm
33. 33.A cuboid is 6 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 74 sq cm (b) 296 sq cm (c) 120 sq cm (d) 148 sq cm
34. 34.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 512 sq cm (d) 384 sq cm
35. 35.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 30 cu cm (d) 1000 cu cm
36. 36.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
37. 37.A cuboid is 11 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 472 sq cm (b) 236 sq cm (c) 944 sq cm (d) 660 sq cm
38. 38.A cuboid is 9 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 450 sq cm (b) 185 sq cm (c) 370 sq cm (d) 740 sq cm
39. 39.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 864 sq cm (c) 144 sq cm (d) 576 sq cm
40. 40.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm

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