If the rectangular prism has a volume of 27 in³, then we know that:
length x width x height = 27
Since it is a rectangular prism, we can assume that the base of the rectangular pyramid is also a rectangle with the same dimensions as the base of the prism.
The height of the pyramid is not given, but we know that it is congruent to the height of the prism. Therefore, the height of the pyramid is also equal to the height of the prism.
The volume of a pyramid is given by the formula:
1/3 x base area x height
Since the base of the pyramid is a rectangle with the same dimensions as the base of the prism, the base area of the pyramid is the same as the base area of the prism. Therefore, we can substitute the base area of the prism into the formula for the pyramid:
1/3 x base area x height = 1/3 x (length x width) x height
Since the height of the pyramid is equal to the height of the prism, we can substitute the height of the prism into the formula:
1/3 x base area x height = 1/3 x (length x width) x height = 1/3 x 27
Simplifying the expression, we get:
1/3 x 27 = 9
Therefore, the volume of the rectangular pyramid is 9 in³.