$\"\"$

\

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

\

Cone is cut by a plane parallel to base and $\"\"$ units above the base.

\

Thus, the rotation is vertical.

\

Draw diagram for the situation :

\

$\"\"$

\

The volume of the solid generated revolving about the $\"\"$ -axis.

\

Washer method: $\"\"$ .

\

Find $\"\"$ .

\

The points are $\"\"$ and $\"\"$ .

\

Line joining the points $\"\"$ and $\"\"$ is

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Here $\"\"$ and $\"\"$ .

\

Integral limits are $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ , $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .