Go look it up in the Nvidia developer stuff. They have specific reasons for not checking Diameter as if it were a box prior to refining and looking for the exact sphere collision.
Also, generally using just the center point and a radius you can figure out the precise intersecrion without PI if you know other parameters (like where the intersection is expected to come from).
The Nvidia stuff is helpful if you are trying to develop your own system or if you just want to learn what works in practice vs what works in theory…