To find the volume \( V \) of the pasta box using the formula \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height, we first need to calculate the area of the base \( B \).
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The dimensions of the pasta box are:
- Length \( l = 2 \frac{1}{2} \) inches = \( 2.5 \) inches
- Width \( w = \frac{1}{2} \) inch = \( 0.5 \) inches
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The area of the base \( B \): \[ B = l \times w = 2.5 \times 0.5 = 1.25 \text{ in}^2 \]
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The height \( h \) is given as \( 8 \frac{1}{2} \) inches = \( 8.5 \) inches.
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Now we can substitute \( B \) and \( h \) into the volume formula: \[ V = B \times h = 1.25 \times 8.5 \]
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Calculate \( 1.25 \times 8.5 \): \[ 1.25 \times 8.5 = 10.625 \]
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Convert \( 10.625 \) to a mixed number: \[ 10.625 = 10 \frac{625}{1000} = 10 \frac{5}{8} \]
Thus, the volume of the pasta box is:
\[ \boxed{10 \frac{5}{8} \text{ in}^3} \]