The volume \( V \) of a pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular prism with the same base area and height as the pyramid, the volume \( V \) of the prism is calculated using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Since the volume of the pyramid is given as \( 10 , \text{cm}^3 \), we can express the volume of the prism in terms of the volume of the pyramid.
If we denote the base area as \( A \) and the height as \( h \), the volume of the pyramid is:
\[ 10 = \frac{1}{3} \times A \times h \]
To find the volume of the prism:
\[ V_{\text{prism}} = A \times h \]
We can find \( A \times h \) from the pyramid's volume equation:
\[ V_{\text{prism}} = 3 \times 10 = 30 , \text{cm}^3 \]
Therefore, the volume of the rectangular prism is \( 30 , \text{cm}^3 \).