The purpose in this problem is to find the radius r and the height h of a cone that maximize the sum of the volume and the surface area of the cone in a sphere with radius R. The sum of these values is calculated as
V+A = πr^2h/3+πr^2+πr√(h^2+r^2)
The optimization problem becomes:
Maximize: V+A = πr^2h/3+πr^2+πr√(h^2+r^2)
Subject to h<2R , r<R
I am not sure if the final form of the problem is correct or not. If it is correct, which algorithm can be applied to solve this optimization problem? Thanks.
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