Answer:
f(r) = r/4
Step-by-step 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
