The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm, is _______ $\mathrm{cm}^3 / \mathrm{cm}^2$.

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Aicharya · Accepted Answer

Volume of sphere $(V)=\frac{4}{3} \pi r^3$ Surface area of sphere $(A)=4 \pi r^2$ $\begin{aligned} & 	herefore \quad \frac{d V}{d r}=4 \pi r^2 	ext { and } \frac{d A}{d r}=8 \pi r \ & 	herefore \quad \frac{d V}{d A}=\frac{\frac{d V}{\frac{d r}{d A}}}{\frac{d r}{d r}}=\frac{4 \pi r^2}{8 \pi r}=\frac{r}{2} \ & 	herefore \quad\left(\frac{d V}{d A}ight)_{r=2}=\frac{2}{2}=1 \mathrm{~cm}^3 / \mathrm{cm}^2 \end{aligned}$

The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm, is…

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