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

Explanation

We know,



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


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


`s=4 pi r^{2}`


`Rightarrow frac{d s}{d r}=8 pi r`


`Rightarrow frac{d v}{d s}=frac{r}{2}=1 text { at } r=2`



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