An inverted cone of radius a and height h is filled with water. A sphere made of a material denser than water is placed in the cone. Find the radius of the sphere, r, that will displace the largest volume of water.

(In reply to Comparing the 3D problem with the 2D analog by Steven Lord)

Very nice analysis.  It's interesting but understandable that the transitions  be the same for 2D vs 3D as it is a function of the radius in both cases, but volume generallyinvolves  a higher power of the radius vs area. 

Posted by Kenny M on 2019-10-01 17:21:39