To compare the volumes of the triangular prism and the triangular pyramid, we can use the formulas for their volumes.
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Volume of a Triangular Prism: \[ V_{prism} = B \cdot h \] where \( B \) is the area of the triangular base and \( h \) is the length of the prism. Given:
- \( B = 10 , \text{in}^2 \)
- \( h = 7 , \text{in} \)
Plugging in the values: \[ V_{prism} = 10 \cdot 7 = 70 , \text{in}^3 \]
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Volume of a Triangular Pyramid: \[ V_{pyramid} = \frac{1}{3} B \cdot h \] where \( B \) is the area of the triangular base and \( h \) is the height of the pyramid. Given:
- \( B = 10 , \text{in}^2 \)
- \( h = 7 , \text{in} \)
Plugging in the values: \[ V_{pyramid} = \frac{1}{3} \cdot 10 \cdot 7 = \frac{70}{3} , \text{in}^3 \]
Now we can compare the volumes:
- Volume of the prism: \( 70 , \text{in}^3 \)
- Volume of the pyramid: \( \frac{70}{3} , \text{in}^3 \)
To find out how the volume of the prism compares to the pyramid: \[ \frac{V_{prism}}{V_{pyramid}} = \frac{70}{\frac{70}{3}} = 70 \cdot \frac{3}{70} = 3 \]
This means the volume of the prism is 3 times the volume of the pyramid.
Therefore, the correct response is: The volume of the prism is three times as large as the volume of the pyramid.