Water is leaking out of an inverted conical tank at a rate of $13400\mathrm{.}0$ cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height $13\mathrm{.}0$ meters and

the diameter at the top is $7\mathrm{.}0$ meters. If the water level is rising at a rate of $18\mathrm{.}0$ centimeters per minute when the height of the water is $1\mathrm{.}5$ meters, find the rate at which water is being pumped into the tank in

cubic centimeters per minute.

Note: Let $"$R$"$ be the unknown rate at which water is being pumped in$.$ Then you know that if $V$ is volume of water, $\frac{dV}{dt}=R-13400\mathrm{.}0.$ Use geometry $($similar triangles?$)$ to find the relationship between the

height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius $r$ and height $h$ is given by $\frac{1}{3}{r}^{2}h.$