Cutting Contrives Conical Cup (Posted on 2005-04-01)
Out of a circular piece of paper, you wish to form a cone cup, so you cut out a circle wedge (with its extreme at the circle center) and join the resulting straight sides, forming a conical cup.
What size should the wedge be, to maximize the capacity of the cone?
Of course as a practical matter, you should cut a wedge smaller that that which is calculated, so you have some overlap on which to add glue to hold the cup together at the maximum volume.
practically speaking
