A rectangular prism has a volume of 27 in.3 . 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, and the base and height of the rectangular pyramid are congruent to the prism, we can say that the length, width, and height of the prism are also the same for the pyramid.
Therefore, if we let x be the length, width, and height of both the prism and the pyramid, then the volume of the pyramid can be calculated using the formula for the volume of a rectangular pyramid, V = (1/3)lwh.
Given that V = 27 in^3, and l = w = h = x, we can substitute these values into the formula:
27 = (1/3)x*x*x
27 = (1/3)x^3
81 = x^3
x = 3
Therefore, the volume of the rectangular pyramid is V = (1/3)(3)(3)(3) = 9 in^3.