To find the volume of the shoebox, we can use the formula \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height.
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Calculate the area of the base \( B \):
- Length \( l = \frac{1}{12} \) ft
- Width \( w = \frac{3}{4} \) ft
The area of the base \( B \) is given by: \[ B = l \times w = \frac{1}{12} \times \frac{3}{4} \]
To multiply these fractions, we multiply the numerators and the denominators: \[ B = \frac{1 \times 3}{12 \times 4} = \frac{3}{48} = \frac{1}{16} \text{ ft}^2 \]
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Now, calculate the volume \( V \):
- Height \( h = \frac{1}{2} \) ft
Using the volume formula: \[ V = B \times h = \frac{1}{16} \times \frac{1}{2} \] Again, we multiply the fractions: \[ V = \frac{1 \times 1}{16 \times 2} = \frac{1}{32} \text{ ft}^3 \]
Thus, none of the provided options directly match the calculated volume of \( \frac{1}{32} \text{ ft}^3 \).
However, it seems we might have made a mistake in interpreting the options. Since \( \frac{1}{32} \text{ ft}^3 \) wasn't an option initially provided, please check for possible rounded options in context (they might be approximately larger in some scenarios) or recalculate from the original measurements if in doubt. But, based on the calculation detail, the answer is indeed \( \frac{1}{32} \text{ ft}^3 \).