A room 1728 cubic metres by volume is represented in a model by a cube of 4 centimetres side. Show the RF of the scale.

The volume of the actual room is $1728 \text{ m}^3$. Since it's represented by a cube in the model, we assume the room is also a cube.
The volume of a cube is given by $V = S^3$, where $S$ is the side length.

$$S^3 = 1728 \text{ m}^3$$

To find $S$, take the cube root of the volume:

$$S = \sqrt[3]{1728 \text{ m}^3}$$ $$S = 12 \text{ m}$$

The side of the model cube is $4 \text{ cm}$.
The side of the actual room is $12 \text{ m}$. Convert meters to centimeters:

$$12 \text{ m} = 12 \times 100 \text{ cm} = 1200 \text{ cm}$$

The RF is the ratio of the length on the drawing (model) to the actual length.

$$\text{RF} = \frac{\text{Length on model}}{\text{Actual length}}$$ $$\text{RF} = \frac{4 \text{ cm}}{1200 \text{ cm}}$$

$$\text{RF} = \frac{4}{1200}$$ $$\text{RF} = \frac{1}{300}$$

The Representative Fraction (RF) of the scale is $\frac{1}{300}$.