The volume \( V \) of a rectangular pyramid is given by the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the rectangular prism has the same base area and height as the pyramid. The volume \( V \) of a rectangular prism is given by the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Since the rectangular prism has the same base area and height as the pyramid, we can express the volume of the prism in terms of the volume of the pyramid:
\[ \text{Volume of Prism} = 3 \times \text{Volume of Pyramid} \]
Given that the volume of the pyramid is \( 10 , \text{cm}^3 \):
\[ \text{Volume of Prism} = 3 \times 10 , \text{cm}^3 = 30 , \text{cm}^3 \]
Thus, the volume of the rectangular prism is
\[ \boxed{30 , \text{cm}^3} \]