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What is the value of the ratio of the surface area to the volume of the cylinder?

What is the value of the ratio of the surface area to the volume of the cylinder?-example-1

1 Answer

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Answer:

2/3

Explanation:

Surface area is ...

... S = 2πr² + 2πrh = 2πr(r+h)

Volume is ...

... V = πr²h

Then the ratio of surface area to volume is ...

... S/V = (2πr(r+h))/(πr²h) = 2(r+h)/(rh)

For r= 4 and h=12, this ratio is

... S/V = 2(4 +12)/(4·12) = 2/3

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Comment on this ratio

Unlike many ratios, this ratio is not a pure number. It has units of 1/ft. That means the ratio would be different if the dimensions of the cylinder were expressed in different units. If the dimensions were in inches, for example, the ratio would be 1/18 per inch.

User Tien Duong
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