To find the volume of the pyramid, we need to know the formula for the volume of a pyramid and compare it with that of a prism.
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Volume of a Prism: The formula for the volume of a prism is: \[ V = B \cdot h \] where \( B \) is the area of the base and \( h \) is the height.
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Volume of a Pyramid: The formula for the volume of a pyramid is: \[ V = \frac{1}{3}B \cdot h \] where \( B \) is the area of the base and \( h \) is the height.
We know:
- The volume of the prism is \( 600 , \text{ft}^3 \).
- The height \( h \) of both the prism and pyramid is the same.
Given that both the prism and pyramid have the same base area, we can calculate the base area \( B \) of the triangle:
\[ B = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 , \text{ft} \times 6 , \text{ft} = 60 , \text{ft}^2 \]
Since the volume of the prism is given: \[ 600 = B \cdot h \] Substituting the base area \( B = 60 \): \[ 600 = 60 \cdot h \] Solving for \( h \): \[ h = \frac{600}{60} = 10 , \text{ft} \]
Now we can calculate the volume of the pyramid using the same base area and height:
\[ V_{\text{pyramid}} = \frac{1}{3}B \cdot h = \frac{1}{3} \times 60 , \text{ft}^2 \times 10 , \text{ft} = \frac{600}{3} = 200 , \text{ft}^3 \]
Thus, the volume of the pyramid is 200 ft.³.
So the correct response is: 200 ft.3 or 200 ft. cubed.