A prism and a pyramid both have this triangular base if both shapes have the same height and the volume of the prism is 1092 cubic units. What is the volume of the pyramid?
Since the prism and pyramid have the same base and height, their volumes are directly proportional to the ratio of their base areas.
The volume of a prism is given by the formula V = Bh, where B is the base area and h is the height. Similarly, the volume of a pyramid is given by the formula V = 1/3 Bh.
Since the base area of the prism is the same as the base area of the pyramid, we can write the ratio of their volumes as:
1092/1 = V/3
V = 3 * 1092
V = 3276
Therefore, the volume of the pyramid is 3276 cubic units.