A circle has radius 9. What is the length of an arc with a central angle of 80°?

Arc length is the fraction $\frac{80}{360}=\frac{2}{9}$ of the circumference. The circumference is $2\pi(9)=18\pi$, so the arc length is $\frac{2}{9}\cdot18\pi=4\pi$, choice A. Choice D ($18\pi$) is the whole circumference. Choice B ($9\pi$) is half the circumference, the arc for $180^\circ$. Choice C ($16\pi$) is $\frac{8}{9}$ of the circumference, which would correspond to an angle of $320^\circ$. A good check is that $80^\circ$ is less than a quarter of the circle, so the arc must be less than $\frac{18\pi}{4}=4.5\pi$.