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'Cuboid Challenge' printed from http://nrich.maths.org/

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From a square sheet of paper 20cm by 20cm, we can make a box without a lid by cutting a square from each corner and folding up the flaps.

 

Find the different volumes of box it is possible to make by varying the size of the cut-out squares.
What is the maximum possible volume?
What is the size of the square cut-out that produces it?


Now try starting with different sized square sheets of paper.

Can you find a relationship between the size of paper and the size of the square cut-out that produces the maximum volume?

Click here for a poster of this problem.