a. A torus is formed by revolving the region bounded by the circle $(x-2)^2 + y^2 = 1$ about the y-axis. Use the disk/washer method to calculate the volume of the torus.
Figure given, showing $r=2$ and with centroid at $(2,0)$
b. Use the disk/washer method to find the volume of the general torus if the circle has radius r and its center is R units from the axis of rotation.
For part a, I started by rewriting equation as $x = 2 \pm \sqrt{1-y^2}$. I was using the washer setup, and simplified to $V= 8\pi \int_{-1}^1 \sqrt{1-y^2}dy$.
The answer is given as $4\pi^2$. Just need to figure out the work to get there.
Again, for part b answer is given as $2\pi^2 r^2 R$. I know I need the answer from part a to solve part b. Looking for any help on how to complete the steps that will give me the answer.
Thanks!