A cylindrical tank with radius $6mis$ being filled with water $at$ a rate $of2\frac{m^3}{m}in.$ How fast $is$ the height $of$ the water increasing?

Step $1$

$Ifhis$ the water's height, the volume $of$ the water $isV=r^{2}h.We$ must find $d\frac{V}{d}t.$ Differentiating both sides $of$ the equation gives the following.

$\frac{dV}{dt}=1$

$\frac{dh}{dt}$

Step $2$

Substituting for $r,$ this becomes $\frac{dV}{dt}=$

$*\frac{dh}{dt}$

Step $3$

Substituting for $\frac{dV}{dt}$ and isolating $\frac{dh}{dt}\frac{m}{?}$ min