The mass of the column of air is approximately \( 16951.02 \, \text{kg} \).
The mass of a column of air can be determined using the formula for pressure:
\[ P = \frac{F}{A} \]
where:
- \( P \) is the pressure,
- \( F \) is the force, and
- \( A \) is the area.
Rearranging the formula to solve for force (\( F \)), we get:
\[ F = P \times A \]
Now, force is related to mass (\( m \)) and acceleration due to gravity (\( g \)) through the equation:
\[ F = m \times g \]
Combining the two equations:
\[ P \times A = m \times g \]
Solving for mass (\( m \)):
\[ m = \frac{P \times A}{g} \]
Substitute the given values:
\[ m = \frac{(1.57 \times 10^5 \, \text{Pa}) \times (1.06 \, \text{m}^2)}{9.8 \, \text{m/s}^2} \]
Now calculate:
\[ m \approx \frac{166220}{9.8} \, \text{kg} \]
\[ m \approx 16951.02 \, \text{kg} \]
So, the mass of the column of air is approximately \( 16951.02 \, \text{kg} \).