Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is `2R/sqrt(3)` . Also find maximum volume.

Explanation

`h^2=R^2-r^2`

Volume of cylinder

`r^2=R^2-h^2`

`pir^2(2h)=2pir^2h`

`2pi(R^2-h^2)h`

`(dv)/(dh)=0`

`d/dx[2pi(R^2-h^2)h]=0`

`(R^2-h^2)+h*(-2h)=0`

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