**Example 2:** Determine the volume
created by rotating the shaded area about the y axis.

**Solution:** As a result of rotating the
shaded area around the y axis, a solid shape will be created. Since
the revolution is about the y axis, we only need to find the coordinate of the shaded area. We proceed by
identifying the differential area as

The centroid of the differential area is located at x/2. With that, we calculate the as

The area of the revolving section is given by the denominator
and is equal to 13.33 in^{2}. Now the enclosed volume is
found as