$\begingroup$Given: Volume 30m^2 Diameter 6x Height H
Calculate the radius of the cylinder such that the Total Surface Area is a maximum? Can someone help me understand this question and point me in the correct direction as I've never had a question like this one.
$\endgroup$11 Answer
$\begingroup$Let's start with what we know.
$V = 30$
$D = 6 * H$
$V = \pi * H * (D/2)^2$
Now we need to find a formula for the surface area of a cylinder as a function of things that we know.
$S = 2 * \pi * (D/2)^2 + \pi * D * H$
You want to find the maximum so you should use one of the tests for extruma that you have learned and find when $dS/dD = 0$ or $dS/dH = 0$. You can substitute for D or H and find the maximum. I'm not going to do the calculation for you but you should be able to work it out from here.
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