Question 708·Medium·Math

The circumference is the distance around a circle. For radius $r$, it equals $2\pi r$, so the given $24\pi$ centimeters gives: $24\pi=2\pi r$.

Divide both sides by $2\pi$ to get the radius: $r=\frac{24\pi}{2\pi}$. Cancel $\pi$: $r=\frac{24}{2}$. Divide: $r=12$.

A sector is the slice cut out by an angle at the circle's center. A full turn is $360^\circ$, so the given $60^\circ$ covers this fraction of the circle: $\frac{60}{360}=\frac16$. The sector takes up that same fraction of the circle's area.

The whole circle's area is $\pi r^2$. Take one-sixth of that area and use $r=12$: $A_{\text{sector}}=\frac16\pi(12)^2$. Taking one-sixth of the circumference instead would give an arc length, not an area.

Type $\frac16(12)^2$ into Desmos to calculate the number multiplying $\pi$. Desmos shows $24$, so the sector's area is $24\pi$ square centimeters. Choice B.