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 the triangular prism (V_prism): \[ V_{\text{prism}} = B \times h \] where \( B \) is the area of the base (10 square inches) and \( h \) is the length (7 inches). \[ V_{\text{prism}} = 10 , \text{in}^2 \times 7 , \text{in} = 70 , \text{in}^3 \]
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Volume of the triangular pyramid (V_pyramid): \[ V_{\text{pyramid}} = \frac{1}{3} B \times h \] where \( B \) is again the area of the base (10 square inches) and \( h \) is the height (7 inches). \[ V_{\text{pyramid}} = \frac{1}{3} \times 10 , \text{in}^2 \times 7 , \text{in} = \frac{70}{3} , \text{in}^3 \approx 23.33 , \text{in}^3 \]
Now we can determine how the volumes compare:
- Volume of the prism: \( 70 , \text{in}^3 \)
- Volume of the pyramid: \( \frac{70}{3} , \text{in}^3 \)
To find the relationship: \[ \frac{V_{\text{prism}}}{V_{\text{pyramid}}} = \frac{70}{\frac{70}{3}} = 3 \]
Thus, the volume of the prism is 3 times as large as the volume of the pyramid.
The correct response is: The volume of the prism is three times as large as the volume of the pyramid.