# Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is  Also find the maximum volume.

Let 'x' be the diameter of the bare of the cylinder and Let 'h' be height of the cylinder.

In

The volume of cylinder,

On differentiating equation (ii) w.r.t h we get,

Again differentiating equation (iii) w.r.t. h we get,

So, V is maximum when

hence, the highest of the cylinder of maximum volume that can be inscribed in a sphere of radius R is

Hence proved

From (i) , we have

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