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Spherical displacement of water (Posted on 2019-09-13) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

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observation | Comment 1 of 9
Since the problem is cylindrically symmetric, I believe it can be reduced to a circle and triangle and a difference of areas. But that's as far as I am willing to drop my olive. 

[Later: no this is wrong. Area further from the central axis is worth more volume than area close to the central axis, when revolved. It is the integral of the area element x 2 pi r that must be maximized, where r is a cylindrical coordinate. It _is_ a 3D problem. My comment above is wrong.]

Edited on September 15, 2019, 4:13 pm
  Posted by Steven Lord on 2019-09-13 09:37:52

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