How many liters of air are in:
a) a room that measures 10.0 ft × 11.0 ft and has an 8.00 ft ceiling?
b) a room that measures 11.0 ft x 11.0 ft and has a 10.0 ft ceiling?
1 in. = 2.54 cm (exactly); 1 l = 103cm3

A) 24916 Lts

B) 34267 Lts

Explanation:

Considering that the air is a gas and this has the ability to expand throughout the whole room, the volume of air will be the same as the volume of the given room.

So, in case A the solution is as follows:

You can think of the volume of the room as the volume of a cube. Having said this, you will have that:

V = Lenght x Height x Width

V = 10.0 ft x 8.0 ft x 11.0 ft

Let's change the units so, afterwards, it becomes easier to obtain the answer in liters as it is asked:

1 mt = 3.28084 ft

Hence:

10 ft = 3.048 mts

8.0 ft = 2.438 mts

11.0 ft = 3.353 mts

Going back to the formula we have:

V = 3.048 mts x 2.438 mts x 3.353 mts = 24.916 mts3

There we have the answer in mts3, but we are asked to obtain the answer in liters so we have to convert it:

Knowing that 1 m3 = 1000 lts

Then: 24.916 mts3 = 24916.22 lts

Now the situation stated in B is the same:

V = 11.0 ft x 10.0 ft x 11.0 ft

Let's change the units according to the conversion described above:

11 ft = 3.353 mts

10.0 ft = 3.048 mts

11.0 ft = 3.353 mts

V = 3.353 mts x 3.048 mts x 3.353 mts = 34.267 mts3

Now, we change the value in mts3 to liters as we did before:

34.267 mts3 = 34267 lts

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