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## Homework Statement

Find the dimensions(r and h) of the right circular cylinder of greatest Surface Area that can be inscribed in a sphere of radius R.

## Homework Equations

[tex]SA=2\pi r^2+2\pi rh[/tex]

[tex]r^2 + (\frac{h}{2})^2 = R^2[/tex] (from imagining it, I could also relate radius and height with [tex]r^2 = h^2 +2R^2[/tex])

## The Attempt at a Solution

[tex]SA=2\pi r^2+2\pi rh[/tex]

[tex]r^2 + (\frac{h}{2})^2 = R^2[/tex]

[tex]h=2\sqrt{R^2-r^2}[/tex]

[tex]SA=2\pi r^2+4\pi r\sqrt{R^2-r^2}[/tex]

[tex]\frac{dSA}{dr}=4\pi r+4\pi (\sqrt{R^2-r^2}+\frac{-2r^2}{2\sqrt{R^2-r^2}})[/tex]

I tried setting that equal to zero, but I wasn't coming up with the right answer

The answer in the book(not mine): [tex]r=\sqrt{\frac{5+\sqrt{5}}{10}}R[/tex]

[tex]h=2\sqrt{\frac{5-\sqrt{5}}{10}}R[/tex]

Can anyone see my error, or did I make one?