Answer
$Time \approx 12minutes$
Work Step by Step
PV = mRT
When ballon is fully inflated, mass of air inside ballon
$m = \frac{PV}{RT}$
Enter the values
$m = \frac{120 \times \frac{4}{3} \times (\frac{15}{2})^{3}}{0.287 \times 293}$
$m = 2521.76 kg$
Flow density
$S = \frac{m}{V} = \frac{P}{RT}$
$S = \frac{120}{0.287 \times297} = 1.427 $
$ Pie = 3.141$
$m^{\circ} = SAV $
$m^{\circ} = 1.427 \times \frac{3.141}{4}(1^{2}) \times 3m/s$
$m^{\circ} = 3.36kg/s$
let time t takes to fill
$m^{\circ} \times t = m$
$t =\frac{m}{m^{\circ}}$
$t = \frac{2521.76}{3.36}$
$t \approx 750 sec$
convert to minutes
$t \approx 12 minutes $
