We know that
[tex]A=200m^2\\h=2.7m\\\upsilon= 5.5m/s\\\%_{air} = 35%[/tex]
So, the volume of the entire building is
[tex]V=2.7*200 = 540m^3[/tex]
The flow capacity of the fan
[tex]\dot{V} = \frac{0.35*540}{60}[/tex]
[tex]\dot{V} = 3.15m^3/min[/tex]
As [tex]1L=10^{-3}m^3,[/tex]
[tex]\dot{V}=3150L/min[/tex]
For the other part we know
[tex]\dot{V}=\frac{\pi d^2}{4}V[/tex]
The diameter is,
[tex]d=\sqrt{\frac{4\dot{V}}{\pi V}}[/tex]
[tex]d=\sqrt{\frac{4*3.15}{\pi* 5.5* 60}}[/tex]
**Note 60 is for the minutes
[tex]d= 0.1101m[/tex]