# Math Help - Finding Minimum Surface Area

1. ## Finding Minimum Surface Area

So I have gotten the equation for the total surface area of a cylinder in term of its radius as:

$T.S.A.=2\pi r^2+\frac{810}{r}$

Where does one begin to even find the minimum surface area of this cylinder? I have to find the minimum surface area graphically on where it appears to have minimum as well as through algebraic (optimisation) methods.

Help appreciated, thanks.

2. ## Re: Finding Minimum Surface Area

surface area is based on a cylinder of fixed volume = 405 units cubed

$S = 2\pi r^2 + \frac{810}{r}$

find $\frac{dS}{dr}$ and set the derivative equal to zero to find the value of $r$ which minimizes $S$

geometrically, graph S and locate the minimum ...

3. ## Re: Finding Minimum Surface Area

Wow, I don't know what I was thinking. That's actually quite easy to do. Thanks for the reply!