The problem gives the diameter of the base. How do you find the radius from the diameter?

Once you have the radius and the height, plug them into $V = \pi r^2 h$ and simplify carefully. Pay attention to squaring the radius and to the order of multiplication.

In a Desmos expression line, type 8/2 to verify that the radius is 4 centimeters.

In a new expression line, type pi*(4^2)*9. Desmos will show a decimal approximation and may also display an exact expression of the form (number)*pi; the number multiplying pi is the volume in cubic centimeters that matches one of the answer choices.

For a right circular cylinder, the volume formula is $V = \pi r^2 h$, where $r$ is the radius of the circular base and $h$ is the height of the cylinder. We are given the height $h = 9$ cm and the base diameter, not the radius.

The diameter of the base is 8 cm. The radius is half the diameter, so $r = 8/2 = 4$ cm. Now we have $r = 4$ and $h = 9$ to use in the formula.

Substitute $r = 4$ and $h = 9$ into $V = \pi r^2 h$: $V = \pi \cdot 4^2 \cdot 9 = \pi \cdot 16 \cdot 9 = \pi \cdot 144$. Therefore, the volume is $144\pi$ cubic centimeters, which corresponds to choice B.