Find the rate of change of the volume of a sphere with respect to its diameter.

Explanation

Let `{V}` and `{r}` be the volume and diameter of the sphere, respectively. Then,



`V=frac{4}{3} pi({P} text { radius })^{3} `


`Rightarrow V=frac{4}{3} pi(frac{r}{2})^{3}=frac{1}{6} pi r^{3} `


`Rightarrow frac{d V}{d r}=frac{1}{2} pi r^{2}`