Prove that the volume of the largest cone, that can be inscribed in a sphere of radius `Rdot\ ` is `8/(27)\ ` of the volume of the sphere.

Explanation

Let the center of the sphere be `O` and radius be `R`. let the height and radius of the variable cone inside the sphere be `h` and `r` respectively


So, in the diagram, `OA=OB=R, AD=h, BD=r`


`OD=AD-OA=h-R`


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