# calculate the radius of the cylinder such that the TSA is a max

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.

• You mean vol is 30 m^3 and diameter is 6 times height already, and area should be minimum or maximum? Not right – Narasimham Mar 10 '16 at 19:10

$V = 30$
$D = 6 * H$
$V = \pi * H * (D/2)^2$
$S = 2 * \pi * (D/2)^2 + \pi * D * H$
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.