A right circular cone of radius ${r}$ and height ${h}$ is to be cut out of a sphere of radius \(

Question

A right circular cone of radius ${r}$ and height ${h}$ is to be cut out of a sphere of radius ${R}$. It is a requirement that the circumference of the base of the cone and its vertex lie on the surface of the sphere. Determine, in exact form in terms of ${R}$, and with full justification, the maximum volume of the cone that can be cut out of this sphere.

Accepted Answer

${V_{\max} = \frac{32\pi R^3}{81}}$

Techniques and Applications Of Differentiation Q6

Techniques and Applications Of Differentiation Q6

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