The mass of the column of air, calculated using the given pressure and area, is approximately 1.696 x 10^4 kg.
To find the mass of the column of air, we can use the formula P = hpg, where P is the pressure, h is the height of the column, p is the density of air, and g is the acceleration due to gravity. In this case, we are given the pressure P = 1.57 x 10^5 Pa and the area A = 1.06 m^2.
Since pressure is force per unit area, we can calculate the force F = PA. Then, using the formula F = mg, where m is the mass and g is the acceleration due to gravity, we can find the mass of the column of air.
Calculate the force F = PA. Given P = 1.57 x 10^5 Pa and A = 1.06 m^2, we have F = (1.57 x 10^5 Pa)(1.06 m^2) = 1.6632 x 10^5 N.
Use the formula F = mg to find the mass m. We know that g = 9.8 m/s^2, so m = F/g. Substituting the values, we get m = (1.6632 x 10^5 N)/(9.8 m/s^2) = 1.696 x 10^4 kg.
Therefore, the mass of the column of air is approximately 1.696 x 10^4 kg.