Once you have the radius, apply the formula for the area of a circle. Do not think about the sector yet; just find the area of the entire circle.

A full circle is $360^\circ$. What fraction of the full circle is a $60^\circ$ sector? Use that fraction of the total area to get the sector's area.

In Desmos, type 24pi/(2pi) and note the value of the result; this is the radius of the circle.

Using the radius from step 1, type pi*(result)^2 (or directly pi*(24pi/(2pi))^2) to get the area of the entire circle.

Now multiply the full area by the fraction 60/360. In Desmos, you can type (60/360)*pi*(24pi/(2pi))^2. The numerical expression that Desmos returns is the area of the $60^\circ$ sector.

The circumference of a circle is given by $C = 2\pi r$.

We are told $C = 24\pi$, so set up the equation:

Now solve for $r$ by dividing both sides by $2\pi$:

So the radius of the circle is 12 centimeters.

The area of a circle is given by $A = \pi r^2$.

Using $r = 12$:

So the area of the whole circle is $144\pi$ square centimeters.

A full circle has an angle of $360^\circ$ at its center.

A sector with a central angle of $60^\circ$ is this fraction of the full circle:

So the sector is $\tfrac{1}{6}$ of the entire circle.

The area of a sector is the same fraction of the circle's area as its angle is of $360^\circ$.

So the sector area is:

Thus, the area of the sector is $24\pi$ square centimeters, which corresponds to choice B.