What is the weight in pounds of the air in rectangular room of volume #3.39xx10^5 " ft"^3#, given the density of air is #rho_"air"=1.29 " kg"/"m"^3#?

1 Answer
Mar 20, 2016

Answer:

The weight is #2.74xx10^4 " lbs"#, which is a little more than the typical large elephant!

Explanation:

First, convert the cubic feet of the room into cubic meters.

#3.39xx10^5 " ft"^3 = 3.39xx10^5 " ft"^3 * ((1 " m")/(3.281 " ft"))^3approx 9,600 " m"^3#

Next, solve the formula for density for mass (in kg).

#rho_"air"="mass"/"volume"#

#"mass "=rho_"air"xx"volume"#
#"mass "=1.29 " kg"/"m"^3xx9,600 " m"^3#
#"mass "=12,384" kg"=1.24xx10^4#

Now, using the fact that #1 " kg"=2.21 " lbs"#, you can find the weight in pounds.

#"mass "=1.24xx10^4" kg"xx(2.21 " lbs")/(1 " kg")=2.74xx10^4 " lbs"#