To find the volume of the brick, we multiply the base area of the brick by its height. Here's a step-by-step solution:
1. Convert the fractional parts to improper fractions:
- The base area is [tex]\( 38 \frac{1}{4} \)[/tex] square inches.
Convert [tex]\( 38 \frac{1}{4} \)[/tex] to an improper fraction:
[tex]\[
38 \frac{1}{4} = 38 + \frac{1}{4} = \frac{38 \times 4}{4} + \frac{1}{4} = \frac{152}{4} + \frac{1}{4} = \frac{153}{4}
\][/tex]
- The height of the brick is [tex]\( 2 \frac{1}{2} \)[/tex] inches.
Convert [tex]\( 2 \frac{1}{2} \)[/tex] to an improper fraction:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{2 \times 2}{2} + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\][/tex]
2. Multiply the base area by the height:
[tex]\[
\text{Volume} = \left(\frac{153}{4}\right) \times \left(\frac{5}{2}\right)
\][/tex]
Multiply the fractions:
[tex]\[
\text{Volume} = \frac{153 \times 5}{4 \times 2} = \frac{765}{8}
\][/tex]
3. Convert the improper fraction to a mixed number:
[tex]\[
\frac{765}{8} = 95 \frac{5}{8}
\][/tex]
Thus, the volume of the brick is [tex]\( 95 \frac{5}{8} \)[/tex] cubic inches.
Therefore, the correct answer is:
[tex]\[
\boxed{95 \frac{5}{8} \text{ cubic inches}}
\][/tex]
