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 in meters?
(a) 157
(b) 284
(c) 382
(d) 628
(e) 764
Solution 1: If the radius is $r$, then the length of an arc of $\theta$ degrees is $2 \pi \frac{\theta}{360} r$. Therefore, in the given problem, we have

$$
2 \pi \frac{300}{360} r=2000 m \Longrightarrow r=2000 \times \frac{3}{5 \pi} \simeq 382.17 m
$$

Thus, the correct option is (c).

Solution 2: Since the circumference has $360^{\circ}$, an arc of $300^{\circ}$ represents $\frac{5}{6}$ of the circumference, so its length is $\frac{5}{6}$ of the circumference, that is:

$$
\frac{5}{6} \times 2 \pi r=2000 m \Longrightarrow r=\frac{2000 \times 6}{10 \pi}=\frac{1200}{\pi} \approx 382.17 \mathrm{~m}
$$