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?
Answer and explanation
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.
Frequently asked questions
What is the correct answer to this question?
\(\frac{660}{\pi}\)
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
