Answer: A

When a central angle is measured in radians, the arc length equals the radius times the angle, so $s = 9 \cdot \frac{2\pi}{3} = 6\pi$ inches. As a check, $\frac{2\pi}{3}$ radians is $120^\circ$, which is $\frac{1}{3}$ of the circle, and $\frac{1}{3}$ of the circumference $18\pi$ is $6\pi$.

Choice D is the area of the sector, $\frac{1}{2}(9)^2\left(\frac{2\pi}{3}\right) = 27\pi$, not the length of the arc.

Why the other choices are wrong

• B. This uses the diameter, 18, in place of the radius, 9.
• C. 18π is the circumference of the whole circle.
• D. 27π is the area of the sector, not the length of the arc.