Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 797 · 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.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) 6 times (d) 3 times
2. 2.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 217 sq cm (d) 144 sq cm
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
5. 5.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
6. 6.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 27 cu cm (d) 36 cu cm
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
8. 8.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 80 cu cm (b) 12 cu cm (c) 48 cu cm (d) 11 cu cm
9. 9.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) 8 times (c) 2 times (d) 4 times
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
14. 14.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) 10 times (c) 25 times (d) 125 times
15. 15.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
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
17. 17.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
18. 18.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
19. 19.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 50 cu cm (c) 100 cu cm (d) 160 cu 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) 8 times (b) 4 times (c) 5 times (d) 2 times
21. 21.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 32 sq cm (b) 64 sq cm (c) 16 sq cm (d) 12 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.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 726 sq cm (c) 121 sq cm (d) 1331 sq cm
24. 24.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 384 cu cm (d) 512 cu cm
25. 25.A cuboid is 10 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 192 cu cm (b) 40 cu cm (c) 160 cu cm (d) 18 cu cm
26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
28. 28.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
29. 29.A cuboid is 8 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 424 sq cm (b) 106 sq cm (c) 144 sq cm (d) 212 sq cm
30. 30.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 54 sq cm (d) 27 sq cm
31. 31.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
32. 32.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
33. 33.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
37. 37.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 84 cu cm (b) 122 cu cm (c) 21 cu cm (d) 14 cu cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 160 cu cm (b) 100 cu cm (c) 10 cu cm (d) 17 cu cm
39. 39.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 486 sq cm (d) 81 sq cm
40. 40.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 344 sq cm (b) 172 sq cm (c) 112 sq cm (d) 86 sq cm

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