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?
Well, unless I've made a mistake here, the maximum capacity cone will be achieved by cutting out a wedge from the circle with a central angle of 2pi[1-(sqrt(6))/3] and discarding it. The remaining piece of the circle can be folded into a cone which should have the maximum possible capacity. This central angle of the to-be-discarded wedge is approximately 66deg3'40.43", using a hand calculator.
This result seems reasonable, intuitively... I wonder if it is correct?
ps Had to edit this, as I can't get the numerical symbols to look right!
Edited on April 1, 2005, 8:20 pm
Edited on April 1, 2005, 8:22 pm