A rectangular prism has volume of 252 in.³. If a rectangular pyramid has a base and height congruent to the prism what is the volume of the pyramid
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 of the prism.
Given that the volume of the rectangular prism is 252 in³, we know that lwh = 252.
Since the rectangular pyramid has the same base and height as the prism, the base area of the pyramid is lw and the height of the pyramid is h.
The volume of a rectangular pyramid is given by the formula V = 1/3 * base area * height. Substituting the values we know, we get:
V = 1/3 * lw * h
Since lwh = 252, we can substitute for lw in the volume formula for the pyramid:
V = 1/3 * (252) * h
V = 84h
Therefore, the volume of the rectangular pyramid with the given dimensions is 84 * h in³.