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?
(1 point)
The volume of a prism is given by the formula V = area of base x height.
In this case, the base of the prism is a triangle with a base of 20 feet and perpendicular height of 6 feet. The area of this triangle is 1/2 x base x height = 1/2 x 20 ft x 6 ft = 60 sq. ft.
Given that the volume of the prism is 600 cubic feet, we can calculate the height of the prism using the formula V = area of base x height.
600 = 60 x height
height = 600 / 60
height = 10 feet
Since the prism and pyramid have the same height, the volume of the pyramid can be calculated using the formula V = 1/3 x area of base x height.
V = 1/3 x 60 sq. ft x 10 ft = 200 cubic feet
Therefore, the volume of the pyramid is 200 cubic feet.