$\"\"$

The curve equations are $\"\"$ , $\"\"$ and $\"\"$ .

Shell method:

The plane region is revolving about the $\"\"$ -axis.

The volume of the solid is $\"\"$ .

Graph:

Graph the region bounded by the curves.

$\"\"$

Observe the graph:

The distance from the center of the rectangle to the axis of revolution is $\"\"$ .

$\"\"$ .

The height of the rectangle is $\"\"$ .

The integrating limits are $\"\"$ to $\"\"$ .

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

$\"\"$

$\"\"$ cubic units.

$\"\"$ cubic units. $\"\"$

$\"\"$ cubic units.