Thank you! That's helped a lot. I think I almost have it now. I can get the outer layers perfectly fine, but the core is still giving me some problems. I'm trying to use the opposite revolve settings but I'm having a hard time getting the core to align with the outer layers. I've tried to revolve in the opposite direction, but that doesn't seem like an option? So if I'm interpreting this correctly, I somehow need to get the position angle just right so that the core aligns with the edges of the layer revolution? Or is this just the nature of the beast, and I need to just adjust it by eye and reposition it until it works?
Revolving the layers:
I made my semicircles, aligned them all to be concentric and then did the 3D revolve effect according to the dialog box in the picture.
Revolving the core:
I tried using the same position angles as I did for the layer revolution, but that didn't work at all. I tried subtracting 100 degrees from the positions but that didn't work either. In the above image I just manually adjusted the cube until it looked more or less like it was kind of aligned.