I have a quick question to help me with some homework.
If I have a cylinder (with only one end, so open at top), how can I measure the minimum amount of surface area for a given Volume.
So far, I have $ A= 2\pi rh + \pi r^2$ and then $ h = \frac{A-\pi r^2}{2 \pi r}$
Not quite sure where to go next...
Hint
Forget about $h= \cdots$ from $A$. You have $$A= 2\pi rh + \pi r^2$$ which you want to minimize. But you also have $$V=\pi r^2h\implies h=\frac{V}{\pi r^2}\implies A=2 \frac V r+\pi r^2$$ Compute its derivative with respect to $r$, set it equal to $0$ since you want an extremum. Use the second derivative test to confirm (or not) that this is a minimum.