If \(s=9\) cm and \( \theta=3 \) radians then what is the radius (r)?
Answer and explanation
Correct answer: 3 cm
The arc-length formula is \(s=r\theta\), where \(\theta\) must be in radians. Thus, \(r=\frac{s}{\theta}=\frac{9}{3}=3\) cm. Therefore, the correct answer is 3 cm. The option 27 cm results from multiplying \(s\) by \(\theta\), whereas finding the radius requires division. Exam tip: For arc-length questions, use \(s=r\theta\) only when the angle is in radians.
Frequently asked questions
What is the correct answer to this question?
3 cm
Why is this the correct answer?
The arc-length formula is \(s=r\theta\), where \(\theta\) must be in radians. Thus, \(r=\frac{s}{\theta}=\frac{9}{3}=3\) cm. Therefore, the correct answer is 3 cm. The option 27 cm results from multiplying \(s\) by \(\theta\), whereas finding the radius requires division. Exam tip: For arc-length questions, use \(s=r\theta\) 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.
