Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 564 · 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) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
2. 2.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 64 cu cm (d) 65 cu cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
4. 4.A cuboid is 12 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 84 cu cm (b) 336 cu cm (c) 23 cu cm (d) 320 cu cm
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
6. 6.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) 5 times (c) 4 times (d) 8 times
7. 7.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
8. 8.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
10. 10.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 14 cu cm (b) 12 cu cm (c) 122 cu cm (d) 84 cu cm
11. 11.A cuboid is 12 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 576 sq cm (b) 288 sq cm (c) 289 sq cm (d) 144 sq cm
12. 12.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) 64 times (c) 4 times (d) 16 times
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
14. 14.If the radius of a circle 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
15. 15.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
17. 17.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) 25 times (c) 10 times (d) 125 times
18. 18.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 97 sq cm (d) 16 sq cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
20. 20.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
21. 21.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) 4 times (c) 8 times (d) 2 times
22. 22.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 15 cu cm (b) 94 cu cm (c) 12 cu cm (d) 60 cu cm
23. 23.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 11 cu cm (b) 8 cu cm (c) 76 cu cm (d) 40 cu cm
24. 24.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 126 sq cm (b) 324 sq cm (c) 162 sq cm (d) 81 sq cm
25. 25.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 400 cu cm (b) 500 cu cm (c) 50 cu cm (d) 25 cu cm
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 64 sq cm (d) 384 sq cm
27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
28. 28.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 9 cu cm (d) 54 cu cm
29. 29.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
31. 31.A cuboid is 12 cm long, 10 cm wide and 5 cm high. What is its volume? (a) 460 cu cm (b) 600 cu cm (c) 120 cu cm (d) 27 cu cm
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
34. 34.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) 6 times (c) 9 times (d) 27 times
35. 35.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
36. 36.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
37. 37.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 92 sq cm (b) 120 sq cm (c) 368 sq cm (d) 184 sq cm
38. 38.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 42 sq cm (b) 164 sq cm (c) 82 sq cm (d) 41 sq cm
39. 39.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
40. 40.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm

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