Question

An auditorium measures 40.0 m 3 20.0 m 3 12.0 m. The density of air is 1.20 kg/m3. What are (a) the volume of the room in cubic feet and (b) the weight of air in the room in pounds?

Answer 1

The volume of the auditorium in cubic feet is 339019.2 ft³. The weight of the air in the room in pounds is 25401.34 lbs, calculated by converting the given dimensions and using the density of the air.

Step-by-step explanation:

To calculate the volume of the auditorium in cubic feet, first find the volume in cubic meters by multiplying the given dimensions: 40.0 m × 20.0 m × 12.0 m = 9600.0 m³. To convert cubic meters to cubic feet, you use the conversion factor 1 m³ = 35.3147 ft³. Thus, the volume in cubic feet is 9600.0 m³ × 35.3147 ft³/m³ = 339019.2 ft³.

To calculate the weight of the air in the room in pounds, first calculate the mass of the air by using the density of the air given: 1.20 kg/m³ × 9600.0 m³ = 11520 kg.

Then, convert this mass to pounds using the conversion 1 kg = 2.20462 lbs. The weight in pounds is therefore 11520 kg × 2.20462 lbs/kg = 25401.34 lbs.

Answer 2

We use the formula,

m = V\rho

Here, m is the mass, V is the volume and
`\rho` density

Also

`V = l w h`

Here l is length, w is width and h is height.

(a) The volume of the room,

`V=40.0 \ m * 3 20.0 \ m * 3 12.0\ m = 3.99 * 10^(6) m^3`

The volume of the room in cubic feet,

`V = 3.99 * 10^(6) m^3 *((3.281 \ ft)/(m) )^3 = 4.3 * 10^7 \ ft^3`

(b) Now the mass of the air in room,

`m= (3.99 * 10^(6) \ m^3) (1.20 \ kg/m^3) = 4.8 * 10^6 kg`.

Therefore, the weight of the air in room,

`W = mg= 4.8 * 10^6 kg * 9.8 m/s^2 = 46.9 * 10^6 \ N \\\\ W = 4.69 * 10^7 \ N`.

The weight of air in the room in pounds,

`W = 4.69 * 10^7 \ N ( (1 \ lb)/(4.448 \ N) ) = 1.1 * 10^7 \ lb`