(a) The volume of a growing spherical shell is $V=\frac{4}{3}\pi r^3$, where the radius $r$ is measured in micrometers ( 1 $\mu$m = $10^{-6}$ m). Find the average rate of change of $V$ with respect to $r$ when $r$ changes from:
(i) 5 to 8 $\mu$m
(ii) 5 to 6 $\mu$m
(iii) 5 to 5.1 $\mu$m

(b) Find the instantaneous rate of change of $V$ with respect to $r$ when $r=5 \mu$m. (Do you notice anything special about this answer?)

**Please leave all your answers in terms of "pi".**

(a) (i) cubic $\mu$m / $\mu$m
     (ii) cubic $\mu$m / $\mu$m
     (iii) cubic $\mu$m / $\mu$m

(b) $V'(5)=$ cubic $\mu$m / $\mu$m