The volume of a rectangular prism is calculated using the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
For a pyramid, the volume is given by:
\[ \text{Volume of Pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the volume of the rectangular pyramid is 10 cm³, we can denote the base area as \( B \) and the height as \( h \). Therefore, we have:
\[ 10 = \frac{1}{3} \times B \times h \]
To find the volume of the rectangular prism with the same base area and height, we can rearrange the pyramid's volume formula. Specifically, the volume of the prism is given by:
\[ \text{Volume of Prism} = B \times h \]
To relate this back to the pyramid's volume, we can rearrange the equation from the pyramid's volume:
\[ B \times h = 3 \times 10 = 30 , \text{cm}^3 \]
Thus, the volume of the rectangular prism is:
\[ \text{Volume of Prism} = 30 , \text{cm}^3 \]
Therefore, the volume of the rectangular prism is 30 cm³.