Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 486 · 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 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
4. 4.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
5. 5.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
6. 6.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
7. 7.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) 9 times (c) 6 times (d) 27 times
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
10. 10.A cuboid is 11 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 61 sq cm (b) 122 sq cm (c) 244 sq cm (d) 66 sq cm
11. 11.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
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
13. 13.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 600 sq cm
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
16. 16.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 61 sq cm (b) 244 sq cm (c) 122 sq cm (d) 84 sq cm
17. 17.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
18. 18.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 8 times (d) 6 times
19. 19.A cuboid is 10 cm long, 9 cm wide and 6 cm high. What is its volume? (a) 408 cu cm (b) 25 cu cm (c) 90 cu cm (d) 540 cu cm
20. 20.A cuboid is 8 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 56 cu cm (b) 262 cu cm (c) 280 cu cm (d) 20 cu cm
21. 21.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 252 sq cm (b) 508 sq cm (c) 254 sq cm (d) 127 sq cm
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
23. 23.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) 10 times (c) 125 times (d) 5 times
24. 24.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 87 sq cm (b) 135 sq cm (c) 174 sq cm (d) 348 sq cm
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
27. 27.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) 4 times (d) 5 times
28. 28.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 80 sq cm (b) 136 sq cm (c) 272 sq cm (d) 68 sq cm
32. 32.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
33. 33.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 144 sq cm
34. 34.A cuboid is 12 cm long, 11 cm wide and 5 cm high. What is its volume? (a) 660 cu cm (b) 132 cu cm (c) 28 cu cm (d) 494 cu cm
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
37. 37.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 64 sq cm (d) 96 sq cm
38. 38.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) 4 times (d) 64 times
39. 39.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 202 sq cm (b) 404 sq cm (c) 168 sq cm (d) 101 sq cm
40. 40.A cuboid is 12 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 768 sq cm (b) 256 sq cm (c) 1024 sq cm (d) 512 sq cm

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