Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 829 · 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 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
2. 2.A cuboid is 9 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 370 cu cm (b) 45 cu cm (c) 24 cu cm (d) 450 cu cm
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
5. 5.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
6. 6.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) 6 times (c) 27 times (d) 9 times
7. 7.A cuboid is 9 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 204 sq cm (b) 408 sq cm (c) 540 sq cm (d) 816 sq cm
8. 8.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
9. 9.A cuboid is 9 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 27 cu cm (b) 17 cu cm (c) 135 cu cm (d) 174 cu cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
12. 12.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) 25 times (d) 10 times
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
14. 14.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 76 cu cm (b) 10 cu cm (c) 40 cu cm (d) 11 cu cm
15. 15.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) 8 times (c) 64 times (d) 16 times
16. 16.A cuboid is 10 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 70 cu cm (b) 210 cu cm (c) 20 cu cm (d) 242 cu cm
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
18. 18.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 144 sq cm (d) 36 sq cm
19. 19.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
20. 20.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm
21. 21.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 60 cu cm (b) 61 cu cm (c) 94 cu cm (d) 12 cu cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
25. 25.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 54 sq cm (d) 27 sq cm
26. 26.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 384 cu cm (d) 512 cu cm
27. 27.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
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.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) 9 times (c) 27 times (d) 6 times
30. 30.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 560 sq cm (b) 300 sq cm (c) 280 sq cm (d) 140 sq cm
31. 31.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 180 sq cm (b) 45 sq cm (c) 90 sq cm (d) 54 sq cm
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
33. 33.A cuboid is 7 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 232 sq cm (b) 464 sq cm (c) 116 sq cm (d) 224 sq cm
34. 34.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) 4 times (c) 5 times (d) 8 times
35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
36. 36.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 30 cu cm
37. 37.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
38. 38.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 54 cu cm (d) 27 cu cm
39. 39.A cuboid is 11 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 135 sq cm (b) 275 sq cm (c) 540 sq cm (d) 270 sq cm
40. 40.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 21 cu cm (d) 196 cu cm

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