What is the mass of air in a room measuring 10.0 m x 5.2 m x 2.5 m, if the density of air is 1.3 `kg//m^3` ?

Answer

To find the mass of air in a room, we can follow these steps:

### Step 1: Calculate the Volume of the Room
The volume \( V \) of the room can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the room:
- Length = 10.0 m
- Width = 5.2 m
- Height = 2.5 m

Substituting the values:
\[ V = 10.0 \, \text{m} \times 5.2 \, \text{m} \times 2.5 \, \text{m} \]
Calculating this gives:
\[ V = 130 \, \text{m}^3 \]

### Step 2: Use the Density to Find the Mass
We know the relationship between mass, density, and volume is given by:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
From this, we can rearrange the formula to find mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Given the density of air is:
\[ \text{Density} = 1.3 \, \text{kg/m}^3 \]
Now substituting the values into the mass formula:
\[ \text{Mass} = 1.3 \, \text{kg/m}^3 \times 130 \, \text{m}^3 \]
Calculating this gives:
\[ \text{Mass} = 169 \, \text{kg} \]

### Final Answer
The mass of air in the room is **169 kg**.

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