The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular pyramid, the base area \( \text{Base Area} \) is given by:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
Given:
- Length = 15 cm
- Width = 9 cm
- Height (altitude) = 21 cm
First, calculate the base area:
\[ \text{Base Area} = 15 , \text{cm} \times 9 , \text{cm} = 135 , \text{cm}^2 \]
Next, substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 135 , \text{cm}^2 \times 21 , \text{cm} \]
Now calculate:
\[ V = \frac{1}{3} \times 2835 , \text{cm}^3 = 945 , \text{cm}^3 \]
Thus, the volume of the rectangular pyramid is:
\[ \boxed{945 , \text{cm}^3} \]