Question 780·Medium·Math

A central angle has its point at the circle’s center. A full turn is $2\pi$ radians, so this angle covers the fraction $\frac{2\pi/3}{2\pi}$ of the circle. The arc takes the same fraction of the circumference as its angle takes of a full turn.

Type $\frac{2\pi/3}{2\pi}$ in Desmos. It shows $0.333\ldots$; tap the fraction button to see $\frac13$. So the angle covers one-third of a full turn.

The given $60\pi$ meters is the circumference, the distance all the way around. The arc length is one-third of that whole: $s=\frac13(60\pi)\text{ meters}$. Don’t take a third of the radius; the arc is part of the circumference.

Keep $\pi$ exact and type $\frac13\cdot60$ in Desmos. It shows $20$. Keep the $\pi$ factor from the circumference, so arc $XY$ is $20\pi$ meters long. Choice B.