If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Start with a $10$ by $10$ grid.
If you cut out each corner square, it could be folded into an
open-top box that had an $8$ by $8$ base and was $1$ square deep.
That means that the box would be able to hold $64$ cubes.
What size square should you cut out of each corner to make the
box that would hold the greatest number of unit cubes?
(Another way to ask this question is 'Which box has the greatest
volume of space available?'.)