Question

The height of a right cylinder is r , where r is the radius. Write a function f in simplest form that represents the ratio of the volume to the surface area.

Answer 1

f(r) = r/4

Explanation:

The volume formula for a cylinder is ...

V = πr^2·h

The total surface area of a cylinder is ...

A = 2πr^2 +2πrh

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

V/A = (πr^2·h)/(2πr(r+h)) = rh/(2(r+h))

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In this problem, we have h = r, so the ratio becomes ...

V/A = r·r/(2(r+r)) = r/4

As a function of r, this is ...

f(r) = r/4