Find the volume that is inside the sphere and outside the cylinder without using integrals. The only information needed is the length of the interior wall that's left in the sphere after the core has been drilled out and one (or more) common geometric formula(s).
1. Find the volume remaining in a sphere of radius R after a core has been removed leaving an interior wall with a length of 8 units without using any integrals?
2. Generalize your answer above when the interior wall has a length of A units?
Not really sure where to start with this, I know how to do it with integrals but I'm completely lost on how to do it without integrals. Any help is greatly appreciated.