The volume of a prism is given by the formula V = (1/2) * base * height. Since the prism has a volume of 600 ft.3 and the base is 20 ft and the height is 6 ft, we can plug these values into the formula to solve for the height of the prism.
600 = (1/2) * 20 * height
600 = 10 * height
height = 60 ft
Since the pyramid has the same base and height as the prism, the volume of the pyramid would be one-third of the volume of the prism.
V(pyramid) = (1/3) * V(prism)
V(pyramid) = (1/3) * 600
V(pyramid) = 200 ft^3
Therefore, the volume of the pyramid is 200 ft^3.
Use the image to answer the question.
An illustration shows a triangle with its base as 20 feet and its perpendicular height as 6 feet.
A prism and a pyramid both 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?
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