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?
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