Given a volume of 1700 cm^3, minimize the surface area of a cylinder.

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

V=$\displaystyle \pi r^2h=1700$

so, for substitutions:

$\displaystyle h=1700/ \pi r^2$, which I can put into the S equation to get:

$\displaystyle S=2 \pi r (1700/r^2) +2 \pi r^2$

And I think I can simplify the above equation to:

$\displaystyle 3400 \pi /r +2 \pi r^2$

and so is the derivative of this equal to:

$\displaystyle -3400 \pi /r^2 +4 \pi r$

I wasn't completely sure if the above equation was right. But continuing on, I would set the derivative equal to 0 and solve for r.

Any help would be greatly appreciated!-I know this is a long post, sorry.