To find the volume of the pasta box using the formula \( V = B \times h \), we first need to determine the base area \( B \) and then multiply it by the height \( h \).
The box is described as having the following dimensions:
- Length (width) = \( \frac{1}{2} \) in
- Height = \( 8 \frac{1}{2} \) in = \( 8.5 \) in
- Depth (length) = \( 2 \frac{1}{2} \) in = \( 2.5 \) in
However, the width mentioned is \( \frac{1}{2} \) in.
First, we calculate the base area \( B \):
\[ B = \text{length} \times \text{width} = 2.5 , \text{in} \times 0.5 , \text{in} = 1.25 , \text{in}^2 \]
Now we can find the volume \( V \):
\[ V = B \times h = 1.25 , \text{in}^2 \times 8.5 , \text{in} \]
Calculating the volume:
\[ V = 1.25 \times 8.5 = 10.625 , \text{in}^3 \]
Now, we can 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:
\[ \boxed{10 \frac{5}{8} , \text{in}^3} \]