A rectangular prism has a volume of 27 inches cubed 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.
Given that the volume of the rectangular prism is 27 inches cubed, we have:
27 = lwh
For a rectangular pyramid with a base and height congruent to the prism, the volume is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height.
Since the base of the pyramid is congruent to the prism, we have B = lw.
Substitute B = lw in the formula for the volume of the pyramid:
V = (1/3)(lw)h
V = (1/3)(27)h
V = 9h
Therefore, the volume of the pyramid is 9 inches cubed.