To find the volume \( V \) of a rectangular prism, you need to use the formula:
\[ V = B \times h \] where \( B = \text{length} \times \text{width} \) and \( h \) is the height.
Given:
- Length = \( 11 \frac{1}{5} \) in.
- Width = \( 9 \frac{1}{2} \) in.
- Height = \( 8 \frac{1}{2} \) in.
First, we need to convert the mixed numbers to improper fractions:
- Length \( 11 \frac{1}{5} = \frac{56}{5} \)
- Width \( 9 \frac{1}{2} = \frac{19}{2} \)
- Height \( 8 \frac{1}{2} = \frac{17}{2} \)
Next, calculate the base area \( B \):
\[ B = \text{length} \times \text{width} = \frac{56}{5} \times \frac{19}{2} \]
Calculating this step-by-step:
- Multiply the numerators: \[ 56 \times 19 = 1064 \]
- Multiply the denominators: \[ 5 \times 2 = 10 \]
- Thus, the base area \( B \) becomes: \[ B = \frac{1064}{10} = \frac{532}{5} \]
Now, we can calculate the volume \( V \):
\[ V = B \times h = \frac{532}{5} \times \frac{17}{2} \]
Again, calculating this step-by-step:
- Multiply the numerators: \[ 532 \times 17 = 9054 \]
- Multiply the denominators: \[ 5 \times 2 = 10 \]
- Thus, the volume \( V \) becomes: \[ V = \frac{9054}{10} = 905.4 \]
Next, convert \( 905.4 \) back to a mixed number: \[ 905.4 = 905 \frac{2}{5} \]
Thus, the volume of the rectangular prism is:
\[ \boxed{904 \frac{2}{5} \text{ in}^3} \]