Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is `cot^(-1)(sqrt(2))dot`

Explanation

`V=1/3pir^2h`

`h=(3V)/(pir^2)`

`CSA=pirl`

`=pirsqrt(h^2+r^2)`

`=pirsqrt((9V^2+pi^2r^6)/(pir^2)`

`CSA=sqrt((9V^2+pi^2r^6)/r`

Differentiate with respect to r

`d/(dr)(CSA)=(3pi^2r^6-9V^2-pi^2r^6)/(r^2sqrt(9V^2+pi^2r^6)=0`

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