To find the volume of the pyramid that has a base and height congruent to the rectangular prism, we use the formula for the volume of a rectangular pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
The volume of the rectangular prism is given as 27 in³. The volume of a rectangular prism is calculated as:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
Since the rectangular pyramid has the same base area and height as the rectangular prism, we can express the volume of the pyramid in terms of the volume of the prism.
Since the pyramid's volume is one-third that of the prism:
\[ V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}} \]
Substituting the volume of the prism:
\[ V_{\text{pyramid}} = \frac{1}{3} \times 27 , \text{in}^3 \]
Calculating this gives:
\[ V_{\text{pyramid}} = 9 , \text{in}^3 \]
Thus, the volume of the pyramid is \( \boxed{9} , \text{in}^3 \).