The Washer Method - Calculus 2

Previously we looked at how to use the disk method, which allowed us to use definite integrals to calculate the volume of solids of revolution. However, all of the solids we looked at so far were complete solids. But what if we had a solid of revolution that featured a hole?

To do this, we use a method known as the washer method, which calculates the volume by adding up the volume of an infinite number of thin washers (or donuts) that would make up the solid.

In this case, the solid of revolution is formed by revolving a region enclosed by two curves around an axis of revolution such as the x-axis, y-axis, or any other line. As such, we will need to determine which of these curves forms the outside of the solid (the outer radius) and which forms the inside of the solid (the inner radius). Identifying each radius is crucial to setting up a definite integral to represent the volume of the solid via the washer method.

In this lesson, you will learn:

• How to use the washer method to calculate volume of solids of revolution formed by revolving a region around the x-axis and y-axis
• The connection between the disk method and washer method
• How to use the washer method to calculate the volume of solids of revolution formed by revolving a region around a line other than the x-axis or y-axis

I hope you find this video to be helpful!

-Josh