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SOVA2 [1]
3 years ago
11

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?
Physics
1 answer:
Burka [1]3 years ago
3 0

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 \times 3 20.0 \ m \times 3 12.0\ m = 3.99 \times 10^{6} m^3

The volume of the room in cubic feet,

V = 3.99 \times 10^{6} m^3 \times(\frac{3.281 \ ft}{m} )^3 = 4.3 \times 10^7 \ ft^3

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

m= (3.99 \times 10^{6} \ m^3) (1.20 \ kg/m^3) = 4.8 \times 10^6 kg.

Therefore, the weight of the air in room,

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

The weight of air in the room in pounds,

W = 4.69 \times 10^7 \ N ( \frac{1 \ lb}{4.448 \ N} ) = 1.1 \times 10^7 \ lb


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