There are many volume-of-a-box questions. I like this one, simpler than what you cite:
Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.
The rectangle might be specialized to a square, as below. See also The Math Forum.
[![BoxVol][1]][1]
(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)