A prism and a pyramid both have a triangular base. If both shapes have the same height and the volume of the prism is 600ft ^3, what is the volume of the pyramid?
The volume of a prism with a triangular base is given by the formula V = (1/2) * base area * height, where the base area is the area of the triangle at the base of the prism.
Since the prism and pyramid have the same height and the same triangular base, they have the same base area. Therefore, if the volume of the prism is 600 ft^3, the volume of the pyramid can be calculated as follows:
V(pyramid) = (1/3) * V(prism)
V(pyramid) = (1/3) * 600 ft^3
V(pyramid) = 200 ft^3
Therefore, the volume of the pyramid is 200 ft^3.