To find 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.
Given the base radius \( r = 2.5 \) in and height \( h = 9 \) in, we can substitute these values into the formula:
\[ V = \pi (2.5)^2 (9) \]
Calculating \( (2.5)^2 \):
\[ (2.5)^2 = 6.25 \]
Now, plug this back into the volume formula:
\[ V = \pi (6.25)(9) \]
Next, calculate \( 6.25 \times 9 \):
\[ 6.25 \times 9 = 56.25 \]
Thus, we have:
\[ V = 56.25 \pi , \text{in}^3 \]
None of the options you provided exactly match the correct expression for the volume of the cylinder, which is \( 56.25 \pi , \text{in}^3 \) or expressed in terms of the original variables, \( V = \pi (2.5)^2 (9) , \text{in}^3 \).
The closest expression from your list would be:
\[ \pi \cdot (2.5)^2 \cdot (9) , \text{in}^3 \]
So the correct representation of the volume of the cylinder is:
\[ \pi (2.5)^2 (9) , \text{in}^3 \]