Since the shape of a can is a cylinder, let be the radius of the base and let be the height of the cylinder.
From given we have , further let be the surface area of the cylinder. And . Our goal is to minimize the surface area.
From the given volume constraint, let's rewrite , plug into the surface formula above, we have:
In order to find the minimum value of , let's find the critical number(s) of the surface function by:
, which gives (please verify it is indeed a minimum)