A right circular cone is inscribed in a sphere. Prove that the volume of the cone cannot exceed ⁸/₂₇ of the volume of the sphere.
One would have asked what I have done on this question but no matter what I did I wasn't making headways I was only moving back and forth.
$V = 4/3πr^3$ , $(πr^2*h )/3$ For sphere and cone.. I have differentiated trying to make some substitutions. ..tried considering those points where the cone touches the sphere. Any clue to this will be appreciated.