Given cylinders of equal surface area, fnd the one with largest Volume.

Attempt:

$\displaystyle V = \pi r^2h$

$\displaystyle A = 2\pi r^2 + 2 \pi rh$

Now I want to use Lagrange multiplier and use the area as a constraint. However, the pi is scaring me. Pi is a constant and so far I have only learnt doing it with variables. I thought of substituting pi with x for example but that is variable. Or should I just treat it as constant and go on with it like this:

$\displaystyle 2rh = 4r$ .......................... I

$\displaystyle r^2 = 2r$ ........................... II

$\displaystyle A = 2\pi r^2 + 2 \pi rh$ ........................... III

From equation I, h = 2r.

Substituting in III, we get $\displaystyle 4\pi r^3 + 4\pi r^2$, which is the same as $\displaystyle \pi r^3 + \pi r^2$

Now I am stuck here.