When air expands adiabatically (without gaining or losing heat), its pressure $P$ and volume $V$ are related by the equation $PV^{1.4}=C$ where $C$ is a constant. Suppose that at a certain instant the volume is $380$ cubic centimeters and the pressure is $89$ kPa and is decreasing at a rate of $8$ kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Answer:

Note: Pa stands for Pascal. One Pa is equivalent to one $\textrm{Newton}/\textrm{m}^2$. kPa is a kiloPascal or 1000 Pascals.