To calculate the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height.
In this case, the base radius \( r \) is 2.5 inches and the height \( h \) is 9 inches. Plugging in these values into the formula:
\[ V = \pi (2.5)^2 (9) \]
Calculating \( (2.5)^2 \):
\[ (2.5)^2 = 6.25 \]
Now substitute back into the volume formula:
\[ V = \pi (6.25) (9) \]
Now, multiply \( 6.25 \) by \( 9 \):
\[ 6.25 \times 9 = 56.25 \]
So the volume is:
\[ V = 56.25\pi , \text{in}^3 \]
Thus, the volume of the cylinder is:
\[ 56.25\pi , \text{in}^3 \]
It can be approximated numerically as \( 176.71 , \text{in}^3 \) if you consider \( \pi \approx 3.14 \).