$\"\"$

\

The radius of the sphere is $\"\"$ .

\

The radius of the cone is $\"\"$ .

\

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

\

Center of the Sphere is $\"\"$ .

\

Draw a digram using the above information.

\

$\"\"$

\

From the diagram.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Apply pythagorean theorem to right angle triangle $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Volume of the cone : $\"\"$

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

Differentiate with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Equate $\"\"$ to zero.

\

$\"\"$

\

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

\

$\"\"$

\

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

\

$\"\"$

\

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

\

$\"\"$

\

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