To find the volume of the rectangular prism that has a congruent base and height to a rectangular pyramid with a volume of 10 cm³, we first need to establish the relationship between the volumes of the pyramid and the prism.
The volume \( V \) of a rectangular pyramid can be expressed as:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the volume of the pyramid is 10 cm³:
\[ 10 = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
From this, we can derive:
\[ \text{Base Area} \times \text{Height} = 30 \quad \text{(multiplying both sides by 3)} \]
Next, the volume \( V \) of a rectangular prism is given by:
\[ V = \text{Base Area} \times \text{Height} \]
Since the prism has the same base area and height as the pyramid, we can substitute \( \text{Base Area} \times \text{Height} \) derived from the pyramid's volume into the prism's formula:
\[ V = \text{Base Area} \times \text{Height} = 30 , \text{cm}^3 \]
Thus, the volume of the rectangular prism is:
\[ \boxed{30 , \text{cm}^3} \]
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