To find the volume of a rectangular prism, the formula used is:
\[ V = B \times h \]
where \( B \) is the base area (length × width) and \( h \) is the height.
Let's calculate the volume for the given dimensions: length = \( 11 \frac{1}{5} \) inches, width = \( 9 \frac{1}{2} \) inches, and height = \( 8 \frac{1}{2} \) inches.
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Convert the mixed numbers into improper fractions:
- Length: \[ 11 \frac{1}{5} = \frac{11 \times 5 + 1}{5} = \frac{55 + 1}{5} = \frac{56}{5} \]
- Width: \[ 9 \frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2} \]
- Height: \[ 8 \frac{1}{2} = \frac{8 \times 2 + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2} \]
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Calculate the base area \( B \): \[ B = \text{length} \times \text{width} = \left( \frac{56}{5} \right) \times \left( \frac{19}{2} \right) \] \[ B = \frac{56 \times 19}{5 \times 2} = \frac{1064}{10} = \frac{532}{5} \]
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Now calculate the volume \( V \): \[ V = B \times h = \left( \frac{532}{5} \right) \times \left( \frac{17}{2} \right) \] \[ V = \frac{532 \times 17}{5 \times 2} = \frac{9054}{10} = 905.4 = 905 \frac{2}{5} \]
Thus, the volume of the rectangular prism is
\[ 904 \frac{2}{5} \text{ in}^3 \]
Therefore, the correct response is:
904 2/5 in³