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](http://mathforum.org/library/drmath/view/53560.html).

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
[![BoxVol][1]][1]
<br />
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
<sup>
(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)
</sup>
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  [1]: https://i.sstatic.net/c322M.jpg