Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

Explanation

Let `{V}` be the volume of the sphere. Then,



`V=frac{4}{3} pi r^{3} `


`Rightarrow frac{d V}{d r}=4 pi r^{2}`



Let `S` be the total surface area of sphere. Then,



`S=4 pi r^{2}`


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