A prism and a pyramid have this triangular base. If both shapes have the same height and the volume of the prism is 600 ft^3, what is the volume of the pyramid?
To find the volume of the pyramid, we can use the formula for the volume of a pyramid, which is (1/3) * base area * height.
Since the prism and pyramid have the same height, and the base of both shapes is a triangle, we can assume they have the same base area. Let's denote the base area of the triangle as A.
The volume of the prism is given as 600 ft^3. Since the volume of a prism is given by base area * height, we can write:
600 = A * height (where height is the height of the prism)
Now, the volume of the pyramid is (1/3) * A * height. Since the heights of the prism and pyramid are the same, the volume of the pyramid can be written as:
Volume of pyramid = (1/3) * A * height = (1/3) * 600 = 200 ft^3
Therefore, the volume of the pyramid is 200 ft^3.