This is I fear also the basis of a question from the Oxford Physics entrance exam from some time in the 1970s or 1980s. I recall  a metric version but otherwise  exactly the same from one of the past papers I looked at when I was looking at old papers to get a feel before sitting the entrance exam myself. ~(*)

The key point is that once you know the length of the cylinder, you can express the radius of the sphere in terms of that length and the diameter of the cylinder bore. What you realise when you write it down, is that the remaining volume ends up  independant of the drill size, as to keep the hole l ngth constant, the sphere gets bigger as the drill does. I could  come back and show it on a bit of paper if it is not obvious.

Mike

(*) now I think they rely more on A level than they used to.

This is I fear also the basis of a question from the Oxford Physics entrance exam from some time in the 1970s or 1980s. I recall  a metric version but otherwise  exactly the same from one of the past papers I looked at when I was looking at old papers to get a feel before sitting the entrance exam myself. ~(*)

The key point is that once you know the length of the cylinder, you can express the radius of the sphere in terms of that length and the diameter of the cylinder bore. What you realise when you write it down, is that the remaining volume ends up  independant of the drill size, as to keep the hole l ngth constant, the sphere gets bigger as the drill does. I could  come back and show it on a bit of paper if it is not obvious.

Mike

(*) now I think they rely more on A level than they used to.