Question 798403
You seem to be going in the right direction.
I'll push you the last fraction of an inch.
For minimum cost, you want C'=0, which  means
{{{16pi*r^2-128pi/r=0}}} --> {{{16pir^2=128pi/r}}} --> {{{16r^3=128}}} --> {{r^3=128/16}}} --> {{{r^3=8}}} --> {{{r=2}}}
So {{{h=20/r^2=20/2^2=20/4=highlight(5)}}}