Volume of cube with three holes

[zgozvrm]

I may be repeating someone here, but I scanned the above posts and didn't see any reference to this:

It may be easier to think of the cube kind of like a Rubik's cube. Cut it into sections such that only a 1/2" cube remains in the center. Determine the volume of the removed parts first. Then work on the center piece separately.

 

[Zamaster]

I mean, we have two solutions, one analytical using calculus, and one geometric numerical. I think this problem has been taken care of? Unless there are other cool methods to solve it.

 

[Bill Crean]

There is nothing wrong with using calculus, of course. When I was given the problem (40 years ago) the statement of the problem indicated no advance maths. or computer programs to be used (there were no PCs then in any case). I think that the calculus method must be much shorter than mine. While the error term in my formula allows me to calculate the solution to any required accuracy, I think it removed elegance to the sectioning method, which could only get the right answer to 2 decimal places.

The person, incidentally, who gave me the problem did not have the solution. I wonder if he ever solved it.

 

[Bill Crean]

Yes, there is another method of solving the problem, as given by a silly old engineering colleague: Fill the holes in the cube with a liquid and then pour the liquid into a measuring cylinder!