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 find the base area. The base area \( A \) of a rectangular pyramid is given by the product of its length and width:
\[ A = \text{Length} \times \text{Width} = 30 , \text{cm} \times 20 , \text{cm} = 600 , \text{cm}^2 \]
Now, using the height of the pyramid (altitude), which is 40 cm, we can substitute into the volume formula:
\[ V = \frac{1}{3} \times 600 , \text{cm}^2 \times 40 , \text{cm} \]
Calculating this gives:
\[ V = \frac{1}{3} \times 24000 , \text{cm}^3 = 8000 , \text{cm}^3 \]
Thus, the volume of the rectangular pyramid is \( \boxed{8000} , \text{cm}^3 \).