Final answer:
The air inside the building weighs 3.9 x 10¹² kg when multiplying the volume of the air (3 x 10⁶ m³) by the weight of 1m³ of air (1.3 x 10⁹ g/m³) and converting the product to kilograms.
Step-by-step explanation:
To calculate the weight of the air inside a building, we can multiply the volume of the air in the building by the weight of 1m³ of air. Given that the weight of 1m³ of air is approximately 1.3 x 10⁹ g and the volume of air inside the building is 3 x 10⁶ m³, we can perform the following calculation:
Weight of air = Volume of air × Weight of 1m³ of air
Weight of air = 3 x 10⁶ m³ × 1.3 x 10⁹ g/m³
Weight of air = 3.9 x 10¹⁵ g
To convert this to kilograms, since there are 1,000 g in a kg, we do the following:
Weight of air in kg = 3.9 x 10¹⁵ g ÷ 1,000 g/kg
Weight of air in kg = 3.9 x 10¹² kg