Find the maximum volume of a cylinder, with total surface area (including two ends) of 2pi
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$\displaystyle 2\pi = 2\pi r h + 2\pi r^2$ solve for h in terms of r, then substitute for h in the volume formula ... $\displaystyle V = \pi r^2 h$ finally, find $\displaystyle \frac{dV}{dr}$ and maximize.
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