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.

If we start by assuming the sphere is small enough to completly fit below the upper lip of the cone then the water displaced equals the volume of the sphere.  However, if this function described in the sentence above ends up not having a local maximum over the range of spheres that fit as described, then we need to consider larger spheres that would not entirely fit in the cone.  These spheres would only displace water by the fraction of thier volume that is below the upper extent of the inverted cone

Posted by Kenny M on 2019-09-13 16:06:06