Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle is one-third that of the cone and the greatest volume of cylinder is `4/(27)pih^3tan^2alphadot`

Explanation

The given right circular cone of fixed height (h) and semi-vertical angle (α) can be drawn as:





Here, a cylinder of radius R and height H is inscribed in the cone.



We have `r=tanh alpha`
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