How to Make Cisterns

Adapted from "Amusements in Mathematics" by Henry Ernest Dudeney.

Given a large sheet of zinc, measuring (before cutting) one metre square,
you are asked to cut out square pieces (all of the same size) from the
four corners of this sheet. You are then to fold up the sides of the
resulting shape, solder the edges and make a cistern. The cistern is open
at the top. You can assume you have the appropriate tools and skill to
carry out the task.

The puzzle is what size should the cut out pieces be, such that the
cistern will hold the greatest possible quantity of water?

I guess a follow on question could be; is it possible to cut out four non-
square pieces (all of the same size and shape), producing a cistern with
tapering sides, which has greater volume. I haven't looked at that yet...
--
David Entwistle