Question

Prove that semivertical angle of a cylinderical cone of given surface area and maximum volume is sin^-1 (1/3).

Answer 1

Let, Slant height of cone = l

Height = h

radius = r

T.S.A. = S

Volume = V

and Semi vertical angle = α

Hence, when semi-vertical angle of cone is sin^-1 (1/3) then its volume will be maximum.