An arc of a circle measures $300^{\circ}$ and its length is $2 \mathrm{~km}$. What is the nearest integer to the measure of the radius of the circle, in meters?
(a) 157
(b) 284
(c) 382
(d) 628
(e) 764
The correct option is (c).

Solution 1: If the radius is $r$, then the length of an arc of $\theta$ degrees is $\frac{2 \pi}{360} \theta r$. Thus, in the given problem, we have that

$$
2000 \mathrm{~m}=\frac{2 \pi}{360} 300 r=\frac{5 \pi}{3} r
$$

therefore $r=2000 \times(3 / 5 \pi) \approx 382.17 \mathrm{~m}$.

Solution 2: Since the circumference has $360^{\circ}$, an arc of $300^{\circ}$ represents $5 / 6$ of the circumference, so its length of $2 \mathrm{~km}$ is $5 / 6$ of the circumference length, that is, $(5 / 6) \times 2 \pi r=2000 \mathrm{~m}$, therefore

$$
r=\frac{2000 \times 6}{10 \pi}=\frac{1200}{\pi} \approx 382.17 \mathrm{~m}
$$