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

From a square sheet of paper $20$ cm by $20$ cm, we can make a box without a lid.

We do this by cutting a square from each corner and folding up the flaps.

Will you get the same volume irrespective of the size of the squares that are cut out?

Investigate what volumes are possible for different sizes of cut-out squares.

What is the maximum possible volume and what size cut produces it?

Try different sized square sheets of paper.

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

Click here for a poster of this problem.