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# Show that semi-vertical angle of the cone of maximum volume and of given slant height is $\tan^{-1} \sqrt 2$.

let ø be the semivertical angle of the right circular cone we know in a right circular cone l²=r²+h²............1 V = 1/3 πr²h V(h)= 1/3 π (l²-h²) h V'(h) = 1/3π (l²-3h²) V'(h)= 0 then l²/3 = h² V''(h) = -2πh V"(h)