$($a$)$ A spherical water$-$tower of radius $15\mathrm{.}1ft$ is half filled. Find the local linear approximation of

the volume of water in the water$-$tower with $V(r)=\frac{2}{3}{r}^3$ and $r=15.$

$($b$)$ Consider a different spherical water$-$tower whose radius is exactly $15ft.$ Water is leaking out

at a constant rate of $80f\frac{t^3}{sec}.$ Given that the volume of water in the water is $V(t)=$

$\frac{}{3}*(h(t){)}^2(3R-h(t)),$ where $R$ is the radius of the water tower and $h(t)$ is the height of the

water level, how fast is the water level dropping when the water level is at $10ft.$

with fully explanation please