Consider a cuboid lecture hall with floor area 400 m2 and 14 m height. the air in the room has a temperature of 14°c, and the pressure at the floor is 0.95 atm. pressure and density distribution in the room are given by the barometric formula. determine the pressures and densities at the ceiling and the floor, the mass of air in the room (hint: needs integration of the density function over height), and thern show that the pressure difference between top and bottom is due to the weight of the air in the room.