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

Explanation

Given


`v=frac{4}{3} pi r^{3} `
`
Rightarrow frac{dv}{dr}=4 pi r^{2} `
`
s=4 pi r^{2} `
`
Rightarrow frac{ds}{dr}=8 pi r `
`
Rightarrow frac{dv}{ds}=frac{r}{2}=1 at r=2`


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