Show that semi-vertical angle of right circular cone of given surface area and maximum volume is.

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Let r be the radius, l be the slant height and h be the height of the cone of given surface area, S. Also, let α be the semi-vertical angle of the cone. Then S = πrl + πr2 Let V be the volume of the cone. Differentiating (2) with respect to r, we get For maximum or minimum, put Differentiating...
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Letrbe the radius,lbe the slant height andhbe the height of the cone of given surface area, S. Also, let α be the semi-vertical angle of the cone. Then S = πrl+ πr2 Let V be the volume of the cone. Differentiating (2) with respect to r, we get For maximum or minimum, put Differentiating again with respect to r, we get Thus, V is maximum when S= 4πr2 As S = πrl+ πr2 ⇒ 4πr2= πrl+ πr2 ⇒ 3πr2= πrl ⇒ l= 3r Now, in ΔCOB, read less
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For all real values of x, the minimum value of  is

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Chiranjeevi
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