Step 1:

\

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

\

Graph the three curves.

\

$\"\"$

\

Observe the graph:

\

The point of intersection of the three curves are $\"\"$ .

\

Region 1 is bounded by the curves $\"\"$ and $\"\"$ between $\"\"$ . \ \

\

Region 1 is bounded by the curves $\"\"$ and $\"\"$ between $\"\"$ .

\

Step 2:

\

The volume of the solid $\"\"$ is $\"\"$ , where $\"\"$ is the cross sectional area of the solid $\"\"$ .

\

$\"\"$

\

For region 1 \ \

\

\

The outer radius of revolution is $\"\"$

\

The inner radius of revolution is $\"\"$ .

\

Integrate under the region $\"\"$ .

\

For region 1 \ \

\

\

The outer radius of revolution is $\"\"$

\

The inner radius of revolution is $\"\"$ .

\

Integrate under the region $\"\"$ .

\

$\"\"$

\

The volume of region bounded by the curves is 20.47834 cubic units.

\

Solution:

\

The volume of region bounded by the curves is 20.47834 cubic units.