Originally Posted by

**billym** Can I just resurrect this delightful thread?

I imagine this is a standard question, but google is so glutted with hyper-physics and stuff these days, its hard to find a standard solution.

I have a liter of water and i want to minimize the surface area of a closed cylinder.

I assume I want to minimize: $\displaystyle S=2\pi rh+2\pi r^2$

with the constraint $\displaystyle V=\pi r^2h=1$

Can somebody start me off if I wanted to use the Lagrange method?

Can I transform S and V so that

$\displaystyle S=f(x,y,z)=$ ...

and

$\displaystyle V=g(x,y,z)=$ ...

Or do I do something else?