A solution
A cylindrical hole 6 inches long has been drilled straight through the center of a solid sphere. What is the volume remaining in the sphere?
(Yes, there’s really enough information to solve this!)
$$36\pi \hspace{2mm} \text{in}^3.$$
(Admittedly, I knew about the Napkin ring problem before answering…)
Correct! Although you may as well have said “I knew the answer before answering”, as that Wiki article gives it away completely! This picture I found (which luckily is a perfect illustration of the problem, down to the numbers) makes it clear what kind of geometry one has to perform to solve this. Nothing too grueling; not even calculus is required!
