Take a square sheet of paper 20cm by 20cm, cut identical squares from each corner, and fold up the flaps to make a box (without a lid).

What is the volume of your box?

What different volumes can you make by varying the size of the squares you cut out?

**What is the maximum possible volume of this type of box that can be made from a 20cm by 20cm square of paper?**

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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