Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 409 · 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 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
2. 2.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
3. 3.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
5. 5.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
9. 9.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 125 sq cm (d) 150 sq cm
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.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
13. 13.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 33 cu cm (d) 1331 cu cm
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
15. 15.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) 8 times (c) 2 times (d) 4 times
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
17. 17.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
18. 18.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
19. 19.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) 3 times (c) 27 times (d) 9 times
20. 20.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 2 times (d) 8 times
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
22. 22.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
23. 23.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
24. 24.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) 4 times (c) 64 times (d) 16 times
25. 25.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 73 sq cm (b) 292 sq cm (c) 90 sq cm (d) 146 sq cm
26. 26.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 144 sq cm (d) 217 sq cm
27. 27.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
28. 28.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 42 sq cm (b) 82 sq cm (c) 164 sq cm (d) 41 sq cm
29. 29.A cuboid is 7 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 620 sq cm (b) 155 sq cm (c) 350 sq cm (d) 310 sq cm
30. 30.A cuboid is 12 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 392 cu cm (b) 60 cu cm (c) 25 cu cm (d) 480 cu cm
31. 31.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 16 cu cm (b) 146 cu cm (c) 18 cu cm (d) 90 cu cm
32. 32.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 65 sq cm (b) 32 sq cm (c) 64 sq cm (d) 128 sq cm
33. 33.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
35. 35.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
36. 36.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
37. 37.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 65 cu cm (d) 96 cu cm
38. 38.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
39. 39.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm
40. 40.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times

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