A prism and a Pyramid both have this triangular 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.
We cannot determine the volume of the pyramid without additional information. The fact that the prism and pyramid have the same base and height does not necessarily mean they have the same volume. It is possible for two shapes with the same base and height to have different volumes, depending on their respective dimensions and shapes.
To find the volume of the pyramid, we need to know the relationship between the volumes of a prism and a pyramid with the same base and height.
The volume of a prism is given by:
Volume Prism = Base Area × Height
Since both shapes have the same triangular base, we can represent the base area of both the prism and the pyramid as "base area".
Given that the volume of the prism is 1,092 cubic units, we can write:
Volume Prism = base area × Height = 1092
Now, let's find the volume of the pyramid.
The volume of a pyramid is given by:
Volume Pyramid = (1/3) × Base Area × Height
Since both the prism and pyramid have the same height and base area, we can substitute these values into the formula:
Volume Pyramid = (1/3) × base area × Height
As we already know that the volume of the prism is 1,092 cubic units, we have:
Volume Pyramid = (1/3) × 1092 = 364 cubic units
Therefore, the volume of the pyramid is 364 cubic units.