A model of a room has a height of 5 cm. The scale is 1:500. The actual floor area of the room is 36 m2. What is the height of the room in the building, and what is the floor area of the model?

The height of the room on the model is $5 \text{ cm}$.
To find the actual height, multiply the model height by the scale factor.

$$\text{Actual height} = \text{Model height} \times \text{Scale factor}$$ $$\text{Actual height} = 5 \text{ cm} \times 500$$ $$\text{Actual height} = 2500 \text{ cm}$$

Since $1 \text{ m} = 100 \text{ cm}$:

$$\text{Actual height in meters} = \frac{2500 \text{ cm}}{100 \text{ cm/m}}$$ $$\text{Actual height in meters} = 25 \text{ m}$$

The height of the room in the building is 25 m.

The actual floor area of the room is $36 \text{ m}^2$.
For areas, the scale factor is squared. So, if the linear scale is $1:k$, the area scale is $1:k^2$.
Here, $k = 500$.

$$\text{Area scale} = \frac{1}{k^2} = \frac{1}{500^2} = \frac{1}{250000}$$

To find the area on the model, divide the actual area by the square of the scale factor.

$$\text{Model area} = \frac{\text{Actual area}}{\text{Scale factor}^2}$$ $$\text{Model area} = \frac{36 \text{ m}^2}{500^2}$$ $$\text{Model area} = \frac{36 \text{ m}^2}{250000}$$ $$\text{Model area} = 0.000144 \text{ m}^2$$

Since $1 \text{ m} = 100 \text{ cm}$, then $1 \text{ m}^2 = (100 \text{ cm})^2 = 10000 \text{ cm}^2$.

$$\text{Model area in cm}^2 = 0.000144 \text{ m}^2 \times 10000 \text{ cm}^2/\text{m}^2$$ $$\text{Model area in cm}^2 = 1.44 \text{ cm}^2$$

The corresponding area on the floor of the model is 1.44 cm².

The height of the room in the building is $\boxed{\text{25 m}}$.
The corresponding area on the floor of the model is $\boxed{\text{1.44 cm}^2}$.