A rectangular prism has a volume of 36 inches cubed. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
Since both the rectangular prism and rectangular pyramid have bases and heights congruent to each other, they are similar shapes. This means their volumes are related by a scale factor.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the volume of the rectangular prism is 36 inches cubed, we can set up the equation: 36 = lwh.
Since the rectangular prism has a base and height congruent to the rectangular pyramid, the volume of the pyramid will be one-third of the volume of the prism.
Therefore, the volume of the rectangular pyramid is 36 / 3 = 12 inches cubed.