Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 246 · 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.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 11 cu cm (c) 78 cu cm (d) 45 cu cm
2. 2.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
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
4. 4.A cuboid is 12 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 23 cu cm (b) 108 cu cm (c) 300 cu cm (d) 216 cu 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.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
7. 7.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
8. 8.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
9. 9.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 576 cu cm (d) 1728 cu cm
10. 10.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) 125 times (d) 25 times
11. 11.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
12. 12.A cuboid is 11 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 110 cu cm (b) 22 cu cm (c) 18 cu cm (d) 174 cu cm
13. 13.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 27 cu cm (d) 729 cu cm
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
15. 15.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
16. 16.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
17. 17.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
18. 18.If the side of a square 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
19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
20. 20.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) 8 times (d) 16 times
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
22. 22.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
23. 23.A cuboid is 12 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 126 sq cm (b) 216 sq cm (c) 504 sq cm (d) 252 sq cm
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
26. 26.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 88 cu cm (c) 14 cu cm (d) 40 cu cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
28. 28.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
30. 30.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 294 cu cm (d) 196 cu cm
31. 31.A cuboid is 8 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 584 sq cm (b) 292 sq cm (c) 336 sq cm (d) 146 sq cm
32. 32.A cuboid is 6 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 192 cu cm (b) 17 cu cm (c) 30 cu cm (d) 180 cu cm
33. 33.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) 2 times (c) 6 times (d) 4 times
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
35. 35.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 56 sq cm (b) 28 sq cm (c) 24 sq cm (d) 112 sq cm
36. 36.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 16 sq cm (d) 97 sq cm
37. 37.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
38. 38.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 14 cu cm (b) 6 cu cm (c) 102 cu cm (d) 54 cu cm
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
40. 40.A cuboid is 11 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 198 cu cm (b) 20 cu cm (c) 33 cu cm (d) 234 cu cm

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