Question

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`?

Answer 1

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"`