Answer
Thus, the volume is increasing at a rate of $35.71$ $cm^{3}/min$
Work Step by Step
Differentiating both sides of
$PV^{1.4}$ = $C$
$1.4PV^{0.4}\frac{dV}{dt}+V^{1.4}\frac{dP}{dt}$ = $0$
$\frac{dV}{dt}$ = $-\frac{V}{1.4P}\frac{dP}{dt}$
$V$ = 400, $P$ = $80$ and $\frac{dP}{dt}$ = $-10$- then
$\frac{dV}{dt}$ = $-\frac{400}{1.4(80)}(-10)$ $\approx$ $35.71$ $cm^{3}/min$
Thus, the volume is increasing at a rate of $35.71$ $cm^{3}/min$
