A room has an actual volume of 120 m³. A model of the room is built using a linear scale of 1:500. Calculate the volume of the model in cm³.

The linear scale is $1:500$. For volumes, the scale factor is cubed.
So, if the linear scale is $1:k$, the volume scale is $1:k^3$.
Here, $k = 500$.

$$\text{Volume scale factor} = 500^3$$ $$\text{Volume scale factor} = 500 \times 500 \times 500$$ $$\text{Volume scale factor} = 125,000,000$$

The volume scale is $1:125,000,000$.

The actual volume of the room is $120 \text{ m}^3$.
To find the model volume, divide the actual volume by the volume scale factor.

$$\text{Model volume} = \frac{\text{Actual volume}}{\text{Volume scale factor}}$$ $$\text{Model volume} = \frac{120 \text{ m}^3}{125,000,000}$$ $$\text{Model volume} = 0.00000096 \text{ m}^3$$

Since $1 \text{ m} = 100 \text{ cm}$, then $1 \text{ m}^3 = (100 \text{ cm})^3 = 1,000,000 \text{ cm}^3$.

$$\text{Model volume in cm}^3 = 0.00000096 \text{ m}^3 \times 1,000,000 \text{ cm}^3/\text{m}^3$$ $$\text{Model volume in cm}^3 = 0.96 \text{ cm}^3$$

The corresponding volume of the model is 0.96 cm³.

The corresponding volume of the model in $\text{cm}^3$ is $\boxed{\text{0.96 cm}^3}$.