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

Sir please solve this as soon as possible..

Let *r* be the radius, *l* be the slant height and *h* be the height of the cone.

∴ Surface area of the cone (S),

Let V be the volume of the cone.

Differentiating (2) w.r.t. *r*, we get–

For maximum or minimum,

⇒ either *r* = 0 or S – 4π*r* ^{2} = 0

Differentiating (3), we have –

Now if α be the semi-vertical angle of the cone, then

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