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?

Responses

400 ft.3
400 ft. cubed

600 ft.3
600 ft. cubed

200 ft.3
200 ft. cubed

1,800 ft.3

1 answer

To find the volume of the pyramid that has the same triangular base and height as the prism, we can use the relationship between the volumes of these two shapes.

The volume \( V \) of a prism is given by the formula:

\[ V = \text{Base Area} \times \text{Height} \]

The volume \( V \) of a pyramid is given by the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Since both shapes have the same base and height, the volume of the pyramid is one-third (1/3) the volume of the prism.

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

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

Thus, the volume of the pyramid is \( 200 , \text{ft}^3 \).

So the correct response is:

200 ft.³ or 200 ft. cubed.