$\"\"$

\

Volume of the cone is $\"\"$ .

\

Draw a cone from the given information.

\

$\"\"$

\

Here,

\

Slant height of the cone : $\"\"$ .

\

Height of the cone : $\"\"$ .

\

Volume of the cone is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Equate derivative to zero.

\

$\"\"$

\

$\"\"$

\

Consider $\"\"$ .

\

Derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

If $\"\"$ , then $\"\"$ .

\

By second derivative test, the volume is maximum at $\"\"$ .

\

Thus, the volume of the cone is maximum at $\"\"$ .

\

$\"\"$

\

The magnitude of $\"\"$ can be found using the formula : $\"\"$ .

\

Substitute the values $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Therefore, the central angle of the sector cut from the circle is equal to $\"\"$ .

\

$\"\"$

\

Therefore,the central angle of the sector cut from the circle is equal to $\"\"$ .