Here's my problem:

I'm trying to figure out how to calculate the volume of this figure:

(Please excuse the crappy drawing).

Anyway, this is a cross section of a "ring". I usually deal with rings with rectangular cross-sections, in which case it is simple to figure out the volume:

volume of "rectangular cross-sectioned ring":

pi/4*(OD^2 - ID^2) * height = volume of ring

Simple.

But for this figure, in order to calculate the total volume, I need 3 volumes:

VLOD - VID - 2*VR = Total volume

Where,

VLOD = pi/4*LOD^2*H

VID = pi/4*ID^2*H

VR = what I don't know how to figure out???

The radius is actually a small portion of a much larger circle, in which I know the coordinates of the center. I'm thinking I need to find the center of gravity of this shape in order to find the area, but I've been looking and looking and looking, and I can't seem to figure this one out.

If anyone can help, I'd greatly appreciate it. Thanks a lot!