Math CentralQuandaries & Queries


Question from Jules, a student:

Dear QQ,
I have the following question :

" A heavy spherical ball is lowered carefully into a full conical wine
glass whose depth is h and whose generating angle (between the axis
and a generator) is w. Show that the greatest overflow occurs when the
radius of the ball is (h*sin(w))/(sin(w)+cos(2w))."


I have solved this problem by taking a cross section when the ball is
fully immersed and by using 2 similar triangles and the pythagorean theorem

I get radius of ball = (h*sin(w))/(1+sin(w))

which is not the same answer as given in the problem. Why ?
Thanks for your help!


It is not clear to me that the ball should be be fully immersed for the largest overflow to occur. If you have h small and w very wide, this gives a very small ball, while a bigger mess would be made by a big ball which touches the rim, and is tangent to the side at the rim.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS