Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 324 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
3. 3.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
4. 4.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 26 sq cm (b) 52 sq cm (c) 104 sq cm (d) 24 sq cm
5. 5.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
8. 8.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 144 sq cm (b) 72 sq cm (c) 73 sq cm (d) 36 sq cm
9. 9.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 48 cu cm (c) 10 cu cm (d) 9 cu cm
10. 10.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) 8 times (c) 5 times (d) 4 times
11. 11.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 16 sq cm (d) 96 sq cm
12. 12.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 324 sq cm (d) 486 sq cm
13. 13.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) 16 times (c) 64 times (d) 4 times
14. 14.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 33 cu cm (d) 1331 cu cm
15. 15.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
16. 16.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 244 sq cm (b) 122 sq cm (c) 61 sq cm (d) 84 sq cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
18. 18.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
19. 19.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 150 sq cm (d) 100 sq cm
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
24. 24.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) 4 times (c) 16 times (d) 64 times
25. 25.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
27. 27.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
28. 28.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
29. 29.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) 3 times (c) 6 times (d) 27 times
30. 30.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 40 sq cm (b) 20 sq cm (c) 80 sq cm (d) 16 sq cm
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 42 cu cm (b) 82 cu cm (c) 12 cu cm (d) 6 cu cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
35. 35.A cuboid is 9 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 106 sq cm (c) 212 sq cm (d) 424 sq cm
36. 36.A cuboid is 12 cm long, 9 cm wide and 5 cm high. What is its volume? (a) 540 cu cm (b) 108 cu cm (c) 26 cu cm (d) 426 cu cm
37. 37.A cuboid is 6 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 30 cu cm (b) 17 cu cm (c) 180 cu cm (d) 192 cu cm
38. 38.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 256 sq cm (d) 512 sq cm
39. 39.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
40. 40.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 576 sq cm (d) 1728 sq cm

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