A hole of radius r is bored through the center of a sphere of radius $R > r$. Find the volume of the remaining portion of the sphere.
I'm not sure on how to approach this problem. What is the most difficult part is knowing how to set up the bounds of integration. Mainly, how does one set up the bounds either when regarding cylindrical shells or washers? How do we exactly arrive at this (is it the points in which we do the sum of the tiny elements of area $dA$)? Is there a "fool-proof" way of knowing the bounds?
I was trying to solve this problem using the washer method in terms of y, but I'm not sure on how to set up my bounds of integration.
Thank you very much for your help in advance.