The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14159.
Given:
- Base radius \( r = 2.5 \) inches,
- Height \( h = 9 \) inches.
Now, substituting the values into the formula:
\[ V = \pi (2.5)^2 (9) \]
Calculating \( (2.5)^2 \):
\[ (2.5)^2 = 6.25 \]
Now substitute it back into the volume formula:
\[ V = \pi (6.25)(9) \]
Calculating \( 6.25 \times 9 \):
\[ 6.25 \times 9 = 56.25 \]
Now, substituting this result:
\[ V = \pi (56.25) \]
To find the numerical value, multiply by \( \pi \):
\[ V \approx 3.14159 \times 56.25 \approx 176.71 \text{ cubic inches} \]
Therefore, the volume of the cylinder is approximately \( 176.71 \) cubic inches.