The volume \( V \) of a rectangular prism can be calculated with the formula:
\[ V_{\text{prism}} = \text{base area} \times \text{height} \]
You mentioned that the volume of the rectangular prism is \( 27 , \text{in}^3 \).
For a rectangular pyramid, the volume \( V \) is given by the formula:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{base area} \times \text{height} \]
Since the base and height of the pyramid are congruent to those of the prism, the base area remains the same, and the height of the pyramid is the same as that of the prism. Therefore, we can relate the two volumes as follows:
Using the prism formula, we can express the base area of the prism (and thus the pyramid) as:
\[ \text{base area} = \frac{V_{\text{prism}}}{\text{height}} = \frac{27}{h} \]
Thus, the volume of the pyramid becomes:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{base area} \times \text{height} \] Substituting in the base area leads to:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \left(\frac{27}{h}\right) \times h \]
This simplifies to:
\[ V_{\text{pyramid}} = \frac{1}{3} \times 27 = 9 , \text{in}^3 \]
Therefore, the volume of the rectangular pyramid is:
\[ \boxed{9 , \text{in}^3} \]