Given the air in a building has a density of 1.184x10^-3 g*cm^-3, how much does the air weigh(in pounds) in a room measuring 30.0 ft and 7.0 in wide by 41.0 ft long by 9.00 ft high?

Answer 1

From the room dimensions, we can find the volume of air. The dimensions are given in feet, so we want to convert all units to centimeters or meters, e.g. because volume is to be in mls or liters, etc. (see units of density).

Room dimensions:

30.0 ft 7.0 in = 367 in x 2.54 cm/in = 932 cm

41.0 ft = 492 in x 2.54 cm/in = 1250 cm

9.00 ft = 108 in x 2.54 cm/in = 274 cm

Volume of room = 932 cm x 1250 cm x 274 cm = 3.19x10⁸ cm3

Mass in grams = 3.19x10⁸ cm3 x 1.184 g/cm3 = 3.78x10⁸ g

Mass in pounds = 3.78x10⁸ g x 1 lb/454 g = 8.33x10⁵ lbs = 833000 lbs = 830,000 lb (2 sif. figs.)