A rectangular prism has a volume of 27 in cubic if a rectangular pyramid has a base and height congruent to the prism
What is the volume of the pyramid
The formula for the volume of a rectangular prism is 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 in^3, we have:
27 = lwh
Since the base and height of the rectangular pyramid are congruent to the prism, the volume of the pyramid can be calculated using the formula for the volume of a pyramid:
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, the base area of the pyramid is the same as the base area of the prism, which is lw. Therefore, the volume of the pyramid is:
V = (1/3)(lw)h
We know that 27 = lwh. Therefore, we can substitute lwh for 27 in the volume formula of the pyramid:
V = (1/3)(27) = 9 in^3
Therefore, the volume of the rectangular pyramid is 9 in^3.