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)
Responses
1,800 ft.3
1,800 ft. cubed
600 ft.3
600 ft. cubed
200 ft.3
200 ft. cubed
400 ft.3
400 ft. cubed
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The volume of a prism is calculated using the formula: base area x height. In this case, the base area of the triangular base is 1/2 x base x height = 1/2 x 20 x 6 = 60 ft². Since the volume of the prism is given as 600 ft.³, we can calculate the height of the prism as 600 ft³ / base area = 600 ft³ / 60 ft² = 10 ft.
Now, the volume of a pyramid is calculated using the formula: 1/3 x base area x height. Given that the base area is 60 ft² and the height is 10 ft, the volume of the pyramid can be calculated as 1/3 x 60 x 10 = 200 ft.³.
Therefore, the volume of the pyramid is 200 ft.³.