Take a sheet of paper 20 cm by 20 cm and make a box without a lid by cutting out a square at each corner and folding up the flaps. What is the volume of your box?
Make boxes with different volumes by varying the sizes of the squares that you cut out.
What is the maximum possible volume?
What is the size of the square cut out to produce it?
Now start with different sized square sheets of paper. What is the relationship between the maximum volume and the size of the square cut out to produce it?
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