### Home > CALC > Chapter 8 > Lesson 8.1.3 > Problem 8-34

Set up an integral that can be used to find the volume of the solid obtained by revolving the region defined below about the -axis.

Notice that BOTH functions are in ______ form. Some students find it easier to visualize

*________ form. Feel free to 'switch the*

*and*

*' in both functions. As long as you switch ALL variables in both equations, the area and volume will be the same either way.*

But you do not have to switch the variables. The semi-circle shape should have been easy to recognize!

Visualize the solid that will be generated after rotating this flag about the -axis. It will look a bit like a donut.

Since the resultant solid has a hole in the center, use the Washer Method:

where is the graph with the longer radius and

*is the graph with the shorter radius.*

Remember that the bounds are -values, not

*-values. That is, unless you switched the*

*and*

*as an initial step.*