This is known as the Theorem of Pappus.
If the radius is b and the distance from the line to the center of the circle is a, then:
By symmetry, the centroid of a circular region is its center. Thus, the distance traveled by the centroid is .
Since the area of a circle is , we get
EDIT: I'm sorry, you said the washer method. The method I posted, is that the one you know?. I would assume. It resembles shells and is most commonly use for these types of problems.
When you're revolving a circle in a torus fashion, the idea is to find the area of the circle and multiply it by the circumference of the circle created when it revolves.
You could do it this way. This is using washers: