Volume of a Spherical Donut

The question posed is this:

Use cylindrical coordinates to find the volume of the solid obtained by drilling a hole of radius 1 through the middle of a sphere of radius 3.

I'm not really sure where to go with this. I've looked at various methods that involve finding the area of the piece removed or using rotation, but I'm still not sure how to actually do it. So far, I've drawn it out and stared at it.

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HINT: You want to revolve the red region in the figure below about the $x$-axis. You’ll need to find the $x$-coordinate of $P$, but otherwise it’s a pretty straightforward volume of revolution problem.