If arc \(s=18\) cm and angle \( \theta=\frac{3}{4} \) radians, what is the radius?
Answer and explanation
Correct answer: 24 cm
When the angle is in radians, the arc-length formula is \(s=r\theta\). Therefore, \(r=\frac{s}{\theta}=\frac{18}{3/4}=18\times\frac{4}{3}=24\) cm. Hence, option C is correct. Option D may result from multiplying \(18\) by \(\frac{3}{4}\), but finding the radius requires division by \(\theta\). Exam tip: In arc-length questions, first check that the angle is expressed in radians.
Frequently asked questions
What is the correct answer to this question?
24 cm
Why is this the correct answer?
When the angle is in radians, the arc-length formula is \(s=r\theta\). Therefore, \(r=\frac{s}{\theta}=\frac{18}{3/4}=18\times\frac{4}{3}=24\) cm. Hence, option C is correct. Option D may result from multiplying \(18\) by \(\frac{3}{4}\), but finding the radius requires division by \(\theta\). Exam tip: In arc-length questions, first check that the angle is expressed in radians.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
