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

200 ft.3
200 ft. cubed

400 ft.3
400 ft. cubed

600 ft.3
600 ft. cubed

1,800 ft.3

Answer 1

To find the volume of the pyramid, we need to use the fact that the volume of a pyramid is one-third of the volume of a prism that has the same base and height.

Given that the volume of the prism is 600 ft³, we can calculate the volume of the pyramid as follows:

\[ \text{Volume of Pyramid} = \frac{1}{3} \times \text{Volume of Prism} \]

Substituting the volume of the prism into the equation:

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

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