To find the volume of a rectangular pyramid, we use the formula:
\[ V = \frac{1}{3} \times B \times h \]
where:
- \( V \) is the volume,
- \( B \) is the area of the base,
- \( h \) is the height.
In this case, the base of the pyramid is rectangular with a width of 4 cm and a length of 9 cm. First, we calculate the area of the base \( B \):
\[ B = \text{width} \times \text{length} = 4 , \text{cm} \times 9 , \text{cm} = 36 , \text{cm}^2 \]
The height \( h \) of the pyramid is given as 21 cm. Now we can substitute these values into the volume formula:
\[ V = \frac{1}{3} \times 36 , \text{cm}^2 \times 21 , \text{cm} \]
Calculating the volume:
\[ V = \frac{1}{3} \times 36 \times 21 \]
Calculating \( 36 \times 21 \):
\[ 36 \times 21 = 756 \]
Now, divide by 3:
\[ V = \frac{756}{3} = 252 , \text{cm}^3 \]
Therefore, the volume of the piece of cheese is \( \boxed{252} , \text{cm}^3 \).