The volume of a rectangular prism is calculated using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
For a pyramid with a rectangular base, the volume is given by:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the volume of the pyramid is 10 cm³, we can set up the equation:
\[ 10 = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
To find the volume of the congruent rectangular prism, we can rearrange the formula for the pyramid and solve for the product of the base area and height:
\[ \text{Base Area} \times \text{Height} = 10 \times 3 = 30 \]
Now, we can substitute this into the formula for the volume of the rectangular prism:
\[ V = \text{Base Area} \times \text{Height} = 30 \text{ cm}^3 \]
Therefore, the volume of the rectangular prism is:
\[ \boxed{30 \text{ cm}^3} \]