#### explain solution rd sharma class 12 chapter 12 derivatives as a rate measure exercise fill in the blanks question 4 maths

Answer: $1\; cm^{^{3}}/cm^{2}$

Hint: Here, we use the volume of surface area of a cone $V=\frac{4}{3}\pi r^{3}$

Solution: $V=\frac{4}{3}\pi r^{3}$

$\Rightarrow \frac{dV}{dr}=3\times \frac{4}{3}\pi r^{2}$

$S=4\pi r^{2}$

$\frac{dS}{dr}=2\times 4\pi r$

$=8\pi r$

$\frac{dV}{dS}=\frac{dV}{dr}\times \frac{dr}{dS}$

$=> \frac{r}{2}=1\; at\; r=2$

So,$1\; cm^{^{3}}/cm^{2}$ is the answer.