 # I have developed the formula to determine the radius of a cylinder with a fixed volume: f ( Agostarawz 2022-07-02 Answered
I have developed the formula to determine the radius of a cylinder with a fixed volume:

Substituted into the formula for the surface area of a cylinder, I get the following function. This would give me the minimum surface area of a cylinder for a given volume.
$S\left(V\right)=2\pi \left(\sqrt{\frac{V}{\pi }}{\right)}^{2}+2\pi \left(2\ast \sqrt{\frac{V}{\pi }}\right)$
However, my assignment for class asks for a rational function for this problem. How could I take my existing function and make it rational?
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I assume the cylinder in question has $h=r$, so that:
$r=\sqrt{V/\pi }$
The surface area is then:
$A=2\pi {r}^{2}+2\pi rh=4\pi {r}^{2}=4\left(\pi V{\right)}^{2/3}$
This of course is not a rational function in $V$ (and never will be), but is a rational function in $r$. Perhaps this is what the assignment means?