Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 864 · 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 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
3. 3.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
4. 4.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 576 sq cm
5. 5.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 343 cu cm (d) 294 cu cm
6. 6.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) 125 times (c) 10 times (d) 25 times
7. 7.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) 8 times (c) 4 times (d) 5 times
8. 8.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
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
11. 11.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 42 cu cm (b) 6 cu cm (c) 82 cu cm (d) 12 cu cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
13. 13.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
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
15. 15.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 75 sq cm (c) 108 sq cm (d) 300 sq cm
16. 16.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 196 sq cm (d) 294 sq cm
17. 17.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) 16 times (c) 4 times (d) 64 times
18. 18.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) 8 times (d) 4 times
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
21. 21.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 726 cu cm
22. 22.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 726 sq cm
23. 23.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 16 cu cm (d) 24 cu cm
24. 24.A cuboid is 8 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 228 sq cm (b) 72 sq cm (c) 57 sq cm (d) 114 sq cm
25. 25.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
26. 26.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
27. 27.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
31. 31.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 31 cu cm (b) 10 cu cm (c) 30 cu cm (d) 62 cu cm
32. 32.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 15 cu cm (d) 150 cu cm
33. 33.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
34. 34.A cuboid is 8 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 16 cu cm (b) 32 cu cm (c) 128 cu cm (d) 160 cu cm
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
36. 36.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
37. 37.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 80 sq cm (b) 96 sq cm (c) 320 sq cm (d) 160 sq cm
38. 38.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) 3 times (c) 6 times (d) 9 times
39. 39.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm

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