Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 340 · 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 every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
2. 2.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 124 cu cm (b) 15 cu cm (c) 72 cu cm (d) 8 cu cm
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
4. 4.If the side of a square 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
5. 5.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 72 sq cm (d) 32 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) 125 times (b) 10 times (c) 25 times (d) 5 times
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
8. 8.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 190 cu cm (b) 18 cu cm (c) 63 cu cm (d) 126 cu cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
10. 10.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 54 sq cm (d) 9 sq cm
11. 11.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 400 cu cm (d) 1000 cu cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
15. 15.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
19. 19.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
20. 20.A cuboid is 10 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 280 cu cm (b) 300 cu cm (c) 60 cu cm (d) 21 cu cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
22. 22.A cuboid is 9 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 764 sq cm (b) 191 sq cm (c) 382 sq cm (d) 504 sq cm
23. 23.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 380 sq cm (b) 95 sq cm (c) 150 sq cm (d) 190 sq cm
24. 24.A cuboid is 8 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 472 sq cm (b) 240 sq cm (c) 118 sq cm (d) 236 sq cm
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
26. 26.A cuboid is 7 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 210 sq cm (b) 420 sq cm (c) 105 sq cm (d) 196 sq cm
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
29. 29.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
30. 30.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 9 cu cm (d) 36 cu cm
31. 31.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
32. 32.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 217 cu cm (d) 144 cu cm
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
35. 35.A cuboid is 9 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 51 sq cm (b) 102 sq cm (c) 204 sq cm (d) 54 sq cm
36. 36.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 36 cu cm (b) 11 cu cm (c) 6 cu cm (d) 72 cu cm
37. 37.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 4 sq cm (d) 24 sq cm
38. 38.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
40. 40.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) 16 times (c) 64 times (d) 4 times

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