Step 3: Machining the Hemispheres
The basic model is easy: use AutoCAD or the equivalent to model the original block, make a sphere of the appropriate diameter, and subtract one from the other. This leaves a block with a hemisphere cut out.
Then, you need to use CAM software to create the toolpaths. You'll want at least two phases: a roughing pass with a large endmill to take away most of the material, and then a finishing pass with the ball end bill to leave a smooth inner surface. Don't try to do the roughing pass with a ball end mill! They don't like being "plunged" directly into metal.
Finally, use the CNC machine to cut the hemispheres. Hopefully, you've learned by practice how to use edge finders, perform air passes, and so on so that you can perform this step safely and accurately. If not, practice some more and find someone to help you!