Posted 15 August 2009 - 09:31 PM

Hi,

I've waded through 12 pages of comments about this puzzle, and I am happy that it is an interesting geometrical puzzle, and that the calculus-based solutions demonstrate that the volume of the remaining 6 inch high donut/bracelet/sliver/whatever shape has a fixed volume of 36pi for all spheres with a diameter greater than 6inches.

However, way back at the start there was the promise of 'logical' solution than did not need calculus. I've not seen it in any of the 12 pages.

Forgive me if I've missed a subtelty somewhere, but the 'logical' solution being offered appears to be based on the premise that the original question does not specify a diameter, therefore the solution does not depend on the diameter, therefore we just have to establish the remaining post-drilled volume for any one particular diameter of sphere, oh look for diameter=6 the answer is 36pi, and voila we have the answer for all diameters.

That's not a complete solution. That's a solution based on a very big, unproven, assumption.

What is the 'logical', non-calculus-based, reasoning that leads us to be able to state in the first place that the solution does not depend on the diameter?