In a circle of radius (14) cm the central angle is \(\frac{3\pi}{7}\). What is the arc length?
Answer and explanation
Correct answer: \(6\pi\) cm
Since the central angle is given in radians, use the arc-length formula \(s=r\theta\). Here, \(r=14\) cm and \(\theta=\frac{3\pi}{7}\). Thus, \(s=14\times\frac{3\pi}{7}=6\pi\) cm. \(7\pi\) cm would result from incorrect simplification of the product. Exam tip: In \(s=r\theta\), the angle \(\theta\) must be in radians.
Frequently asked questions
What is the correct answer to this question?
\(6\pi\) cm
Why is this the correct answer?
Since the central angle is given in radians, use the arc-length formula \(s=r\theta\). Here, \(r=14\) cm and \(\theta=\frac{3\pi}{7}\). Thus, \(s=14\times\frac{3\pi}{7}=6\pi\) cm. \(7\pi\) cm would result from incorrect simplification of the product. Exam tip: In \(s=r\theta\), the angle \(\theta\) must be in radians.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
