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 – 4πr ² = 0

Differentiating (3), we have –

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