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?

(In reply to re(2): Extension to this problem... -- numerical solution by Hugo)

Erm... Why Hugo?

Here in Botswana I'm only waking up, so maybe I'm not thinking clearly, but I agree that an angle of 0 should give two volumes of zero.  Which of the two 'cones' the one with the zero angle, or the one with 360deg angle has the non-zero volume?

I found the same numerical solution, but was hoping one of you guys/gals could solve the dV/dè = 0 equation you get as I find numerical solutions a bit unfulfilling...

Posted by Alec on 2005-04-10 07:42:38