The volume \( V \) of a rectangular pyramid is given by the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular prism (also known as a rectangular cuboid), the volume \( V \) is given by the formula:
\[ V = \text{Base Area} \times \text{Height} \]
If the rectangular prism has a congruent base and height to the pyramid, then the base area and height of the prism are the same as those of the pyramid.
Since the volume of the pyramid is \( 10 \text{ cm}^3 \), we can express this in terms of the base area and height:
\[ 10 = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
To find the volume of the prism, we multiply the volume of the pyramid by 3 (since the pyramid's volume is one-third of the prism's volume):
\[ V_{prism} = 3 \times V_{pyramid} \] \[ V_{prism} = 3 \times 10 = 30 \text{ cm}^3 \]
Therefore, the volume of the rectangular prism is 30 cm³.