The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we need to calculate the area of the base of the pyramid, which is a rectangle. The area \( A \) of a rectangle is given by:
\[ A = \text{length} \times \text{width} \]
In this case, the dimensions of the base are:
- Width = 4 cm
- Length = 9 cm
So the area of the base is:
\[ A = 4 , \text{cm} \times 9 , \text{cm} = 36 , \text{cm}^2 \]
Next, we plug the area of the base and the height into the volume formula:
- Base Area = 36 cm²
- Height = 21 cm
Thus, the volume \( V \) is calculated as follows:
\[ V = \frac{1}{3} \times 36 , \text{cm}^2 \times 21 , \text{cm} \]
Calculating this yields:
\[ V = \frac{1}{3} \times 756 , \text{cm}^3 = 252 , \text{cm}^3 \]
Therefore, the volume of the piece of cheese is:
\[ \boxed{252} , \text{cm}^3 \]