Water is leaking out of an inverted conical tank at a rate of $9600.0$ $\textrm{cm}^3/\textrm{min}$ at the same time that water is being pumped into the tank at a constant rate. The tank has height $7.0 \ \textrm{m}$ and the the diameter at the top is $5.0 \ \textrm{m}$. If the water level is rising at a rate of $22.0 \ \textrm{cm}/\textrm{min}$ when the height of the water is $1.5 \ \textrm{m}$, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answer: $\textrm{cm}^3/\textrm{min}$