A rectangular prism has a base area of 15 cm2 , and pyramid with a congruent base and height has a volume of 20 cm3 . What is the height of the rectangular prism?
Let the dimensions of the base of the rectangular prism be \( l \) and \( w \), where \( lw = 15 \) cm\( ^2 \).
The volume of a rectangular prism is given by \( V = lwh \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height. Since the base area is 15 cm\( ^2 \), we have \( lw = 15 \) cm\( ^2 \), and the volume of the rectangular prism is also given by \( 15h \).
Now, the volume of a pyramid is given by \( V = \frac{1}{3}Ah \), where \( A \) is the base area, and \( h \) is the height. Since the base area of the pyramid is 15 cm\( ^2 \), we have \( A = 15 \) cm\( ^2 \). The volume of the pyramid is 20 cm\( ^3 \), so we have:
\[ 20 = \frac{1}{3} \times 15 \times h \]
\[ 20 = 5h \]
\[ h = 4 \]
Therefore, the height of the rectangular prism is 4 cm.