Use the image to answer the question.

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

400 ft.3
400 ft. cubed

200 ft.3
200 ft. cubed

1,800 ft.3
1,800 ft. cubed

600 ft.3

Answer 1

To find the volume of the pyramid, we can use the relationship between the volumes of a prism and a pyramid with the same base area and height. The volume of a pyramid is one-third the volume of the prism.

Given that the volume of the prism is \( 600 , \text{ft}^3 \):

\[ \text{Volume of the pyramid} = \frac{1}{3} \times \text{Volume of the prism} \]

\[ \text{Volume of the pyramid} = \frac{1}{3} \times 600 , \text{ft}^3 = 200 , \text{ft}^3 \]

Thus, the volume of the pyramid is 200 ft.³.