To determine the volume of a rectangular prism with the given dimensions, we will follow these steps:
1. Convert the mixed numbers into improper fractions:
- Length: [tex]\(10 \frac{2}{5}\)[/tex]
[tex]\[
10 \frac{2}{5} = 10 + \frac{2}{5} = \frac{50}{5} + \frac{2}{5} = \frac{52}{5}
\][/tex]
- Width: [tex]\(8 \frac{1}{2}\)[/tex]
[tex]\[
8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2}
\][/tex]
- Height: [tex]\(6 \frac{1}{4}\)[/tex]
[tex]\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\][/tex]
2. Calculate the base area: (Base Area = Length * Width)
[tex]\[
\text{Length} \times \text{Width} = \frac{52}{5} \times \frac{17}{2} = \frac{52 \times 17}{5 \times 2} = \frac{884}{10}
\][/tex]
Simplify [tex]\(\frac{884}{10}\)[/tex]:
[tex]\[
\frac{884}{10} = 88.4 \, \text{(decimal form)}
\][/tex]
3. Calculate the volume: (Volume = Base Area * Height)
[tex]\[
\text{Base Area} \times \text{Height} = 88.4 \times \frac{25}{4}
\][/tex]
First, convert [tex]\(88.4\)[/tex] to an improper fraction:
[tex]\[
88.4 = \frac{884}{10}
\][/tex]
Now, multiply:
[tex]\[
\frac{884}{10} \times \frac{25}{4} = \frac{884 \times 25}{10 \times 4} = \frac{22100}{40} = 552.5 \, \text{(decimal form)}
\][/tex]
4. Convert the volume back to a mixed number:
The decimal [tex]\(552.5\)[/tex] can be expressed as the mixed number [tex]\(552 \frac{1}{2}\)[/tex].
Therefore, the volume of the rectangular prism is:
[tex]\[
552 \frac{1}{2} \, \text{in}^3
\][/tex]
