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 the maximum volume.

Explanation

`text(Radius of the sphere = R. Let x be the diameter of the cylinder and h be the height)`




`text(Then ) h^2+x^2=(2R)^2=4R^2`



`text(volume of cylinder = ) pi (radius)^2(height)`
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