# Thread: Volume and Surface Area

1. ## Volume and Surface Area

Find the maximum volume of a cylinder, with total surface area (including two ends) of 2pi

2. $2\pi = 2\pi r h + 2\pi r^2$

solve for h in terms of r, then substitute for h in the volume formula ...

$V = \pi r^2 h$

finally, find $\frac{dV}{dr}$ and maximize.