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I have developed the formula to determine the radius of a cylinder with a fixed volume:

$$ f(x) = \sqrt[3]{\dfrac{V}{\pi}}\ $$

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.

$$ S(V) = 2\pi(\sqrt[3]{\dfrac{V}{\pi}})^2+2\pi(2 * \sqrt[3]{\dfrac{V}{\pi}}) $$

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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    What's the height of the cylinder? what is $x$? please explain yourself.2012-05-06
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    note that the units in your derivation are wrong: you can't add two numbers with different dimensions.2012-05-06

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