The volume of the dining room is 2625 m3 . If the mass of air in the room is 3412.5 kg, then what is thedensity of air?

1. Break Down the Problem

To find the density of air, we need to use the formula for density, which is defined as the mass per unit volume. Therefore, we will need to divide the mass of the air in the room by the volume of the room.

2. Relevant Concepts

The formula for density ($\rho$) is: $\rho = \frac{m}{V}$ where:

• $\rho$ = density (kg/m³)
• $m$ = mass (kg)
• $V$ = volume (m³)

3. Analysis and Detail

Given:

• Mass of air, $m = 3412.5$ kg
• Volume of room, $V = 2625$ m³

Using the formula for density, we substitute the values: $\rho = \frac{3412.5 \text{ kg}}{2625 \text{ m}^3}$

Calculating the density: $\rho = \frac{3412.5}{2625} \approx 1.2992 \text{ kg/m}^3$

4. Verify and Summarize

The calculations appear correct as we have performed a straightforward division of mass by volume.

Final Answer

The density of air in the dining room is approximately $1.30 \, \text{kg/m}^3$.