Prove that the radius of the base of right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half that of the cone
Let VAB be the cone of base of radius , r = OA and height , h = VO.
Let a cylinder of base of radius OC = x be inscribed in the cone.
From the figure , it is clear that ΔVOB∼ΔB'DB
Let S be the curved surface area of cylinder.
Then, S= 2(OC) (B'D)
For maximum or minimum values of S, we must have