Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 519 · 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 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
3. 3.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) 10 times (c) 125 times (d) 25 times
4. 4.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 12 cu cm (d) 65 cu cm
5. 5.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 217 sq cm (d) 36 sq cm
6. 6.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) 125 times (c) 10 times (d) 25 times
7. 7.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 202 cu cm (b) 168 cu cm (c) 21 cu cm (d) 18 cu 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) 5 times (b) 2 times (c) 4 times (d) 8 times
9. 9.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
10. 10.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 54 cu cm (d) 27 cu cm
11. 11.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 121 sq cm
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
13. 13.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
14. 14.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 216 sq cm (b) 123 sq cm (c) 492 sq cm (d) 246 sq cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
17. 17.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
18. 18.A cuboid is 11 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 185 sq cm (b) 462 sq cm (c) 370 sq cm (d) 740 sq cm
19. 19.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
20. 20.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 512 sq cm (d) 384 sq cm
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
23. 23.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 196 cu cm (d) 21 cu cm
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
26. 26.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) 3 times (c) 9 times (d) 6 times
27. 27.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 144 sq cm (c) 36 sq cm (d) 73 sq cm
28. 28.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 726 cu cm
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
30. 30.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
31. 31.A cuboid is 11 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 148 sq cm (b) 74 sq cm (c) 88 sq cm (d) 296 sq cm
32. 32.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
35. 35.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 64 sq cm (b) 112 sq cm (c) 224 sq cm (d) 56 sq cm
36. 36.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 512 cu cm (c) 24 cu cm (d) 256 cu cm
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
38. 38.A cuboid is 12 cm long, 11 cm wide and 2 cm high. What is its volume? (a) 25 cu cm (b) 132 cu cm (c) 264 cu cm (d) 356 cu cm
39. 39.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
40. 40.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times

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