To find the volume of the pyramid, we first need to understand the relationship between the volume of a prism and the volume of a pyramid that share the same base and height.
The formula for the volume of a prism is:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
The formula for the volume of a pyramid is:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the volume of the prism is 600 ft³, we can deduce that the formula gives:
\[ 600 = \text{Base Area} \times \text{Height} \]
Next, we need to find the base area of the triangular base. The area of a triangle is given by:
\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
In our case, the base is 20 feet and the height is 6 feet:
\[ \text{Base Area} = \frac{1}{2} \times 20 \times 6 = \frac{1}{2} \times 120 = 60 , \text{ft}^2 \]
Now we can use this area to find the height of the prism. We previously established that:
\[ 600 = \text{Base Area} \times \text{Height} \]
Substituting the base area:
\[ 600 = 60 \times \text{Height} \]
Now, solving for the height:
\[ \text{Height} = \frac{600}{60} = 10 , \text{ft} \]
Now we can find the volume of the pyramid. Using the height we found (10 ft) and the base area calculated (60 ft²):
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] \[ V_{\text{pyramid}} = \frac{1}{3} \times 60 \times 10 = \frac{600}{3} = 200 , \text{ft}^3 \]
Therefore, the volume of the pyramid is 200 ft³.
The correct response is: 200 ft.³.