Sphere in a cone (ball in a wine glass)

[rcgldr]

sphere in a cone (ball in a martini glass)

A problem a friend mentioned to me years ago.

You have a cone with height H and angle A. What is the radius R of a sphere that when placed in the cone, displaces the most volume?

One suggestion was to reduce this to a two dimensional case.

 

[benorin]

Yeah, rotational symmetry would allow reduction to the 2-d case; so, set it up: what's the equation of a cone of angle A? the equation of the circle of radius R circumscribed therein? do the integral, get it in terms of R, differentiate w.r.t. R and set equal to 0.

 

[DaveC426913]

Correction: ball in a martini glass.

Glad I could help.