Copyright © University of Cambridge. All rights reserved.

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

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.