Show that semi-vertical angle of right circular cone of given total surface area and maximum volume is `sin^(-1)""(1)/(3)`.

Explanation

Let `r,h,l` be the radius, height and slant height of the right circular cone respectively.


Let `s` be the given surface area of the cone.


we have, `l^2=r^2+h^2`........(1)


`s=pirl+pir^2`


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