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Cylinder standing on paper sheet
A cylindrical container, like the tin cans used to package some food, can be made by using two circles for the ends and a rectangle which wraps round to form the body.

To make cylinders of varying sizes, the three pieces can be cut from a single rectangle of flat sheet in several ways. For example:

three possible ways to cut a cylinder from A4 paper


Your task is to cut out one rectangle and two circles from a single sheet of A4 paper to make a cylinder with the greatest possible volume.

What are its dimensions?

(We will assume that the dimensions of an A4 sheet of paper are $21$cm and $29.6$ cm)

Click here for a poster of this problem.