A prism and a pyramid both have this triangular base. If both shapes have the same height in the volume of a prism is 600 ft.³. What is the volume of the pyramid?
Measurements: 6ft and 20ft
The volume of a prism is given by the formula V = (1/2) * base * height. In this case, the base of both the prism and the pyramid is a triangle with base 6 ft and height 20 ft.
For the prism, the volume is 600 ft³. Therefore, we can plug in the values into the formula:
600 = (1/2) * 6 * 20
600 = 60
This means that the area of the base of the prism is 60 ft².
Now, we can calculate the volume of the pyramid using the formula V = (1/3) * base * height. Since the base of the pyramid is the same triangle as the prism, the base area remains 60 ft². Therefore, we can calculate the volume of the pyramid as:
V = (1/3) * 60 * 20
V = 400 ft³
Therefore, the volume of the pyramid is 400 ft³.