How to calculate the center of gravity of a cylinder segment?

I have a 6" thick segment of a cylinder, with about a 15' radius to the outer face. It's roughly 10 feet tall, and I'm trying to work out the center of gravity so I can successfully hang it from two points. The inner and outer face weigh the same, and the internal construction is uniform, so any slice through it has a CoG 3" from the face.

It's been a while since I've used calculus and while I'm sure there's a way to do this with pure math, so hoping someone has the math laying around.

(The geometric solution I'm going to try is to find the point where the CoG line (curve) has the same length available on either side of a line drawn through.)