Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 903 · 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 radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
3. 3.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
4. 4.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) 4 times (c) 64 times (d) 8 times
5. 5.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
6. 6.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
7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
8. 8.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) 4 times (c) 8 times (d) 5 times
9. 9.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 40 cu cm (c) 76 cu cm (d) 11 cu cm
10. 10.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
11. 11.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
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) 64 times (b) 8 times (c) 16 times (d) 4 times
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
16. 16.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 864 cu cm (d) 576 cu cm
17. 17.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 88 sq cm (b) 44 sq cm (c) 176 sq cm (d) 48 sq cm
18. 18.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
19. 19.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) 9 times (c) 3 times (d) 27 times
20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 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) 27 times (b) 6 times (c) 3 times (d) 9 times
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
23. 23.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 294 cu cm (d) 21 cu cm
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
25. 25.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) 27 times (d) 9 times
26. 26.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 88 cu cm (b) 48 cu cm (c) 12 cu cm (d) 24 cu cm
27. 27.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
28. 28.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
29. 29.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 31 sq cm (b) 30 sq cm (c) 62 sq cm (d) 124 sq cm
30. 30.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 132 cu cm (c) 36 cu cm (d) 72 cu cm
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
32. 32.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 112 sq cm (c) 224 sq cm (d) 60 sq cm
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
34. 34.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
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
36. 36.A cuboid is 8 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 112 sq cm (c) 64 sq cm (d) 56 sq cm
37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
38. 38.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 1000 cu cm (c) 600 cu cm (d) 30 cu cm
39. 39.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 864 sq cm
40. 40.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 81 sq cm (b) 126 sq cm (c) 324 sq cm (d) 162 sq cm

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