Walking (550) m on a circular path subtends an angle of \(\frac{5\pi}{6}\) at the center. What is the radius of the path?

Correct answer: \(\frac{660}{\pi}\)

For arc length, \(s=r\theta\), where \(\theta\) must be measured in radians. Here \(s=550\) and \(\theta=\frac{5\pi}{6}\). Hence, \(r=\frac{s}{\theta}=\frac{550}{5\pi/6}=\frac{550\times6}{5\pi}=\frac{660}{\pi}\) m. Therefore, option D is correct. The value \(\frac{630}{\pi}\) may result from an error while multiplying or simplifying the fractions. Exam tip: Apply \(s=r\theta\) directly only when the angle is in radians.