A prism and a pyramid both have this rectangular base. If both shapes have the same height and the volume of the prism is 1,092 cubic units, what is the volume of the pyramid?
Since both the prism and pyramid have the same height, their volumes are directly proportional to the area of their bases.
Let the volume of the pyramid be V cubic units and the area of the rectangular base be A square units.
The volume of a prism is given by V = A * h where h is the height. Given that the volume of the prism is 1,092 cubic units and the height is the same for both shapes, we have 1,092 = A * h.
The volume of a square pyramid is given by V = (1/3) * A * h.
Since the height and area of the base are the same for both shapes, we can compare their volumes:
V_pyramid / V_prism = (1/3) * A * h / (A * h) = 1 / 3.
Therefore, the volume of the pyramid is 1/3 of the volume of the prism:
V_pyramid = (1/3) * 1,092 = 364 cubic units.
So, the volume of the pyramid is 364 cubic units.