An arc is \(12\pi\) cm and it subtends an angle \( \frac{3\pi}{4} \) radians at the same radius. What is the radius?
Answer and explanation
Correct answer: 16 cm
The arc-length formula is \(s=r\theta\), where \(\theta\) must be in radians. Thus, \(r=\frac{s}{\theta}=\frac{12\pi}{3\pi/4}=12\pi\times\frac{4}{3\pi}=16\) cm. Therefore, option C is correct. An error such as choosing 12 cm can result from dividing incorrectly by \(\frac{3\pi}{4}\). 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?
16 cm
Why is this the correct answer?
The arc-length formula is \(s=r\theta\), where \(\theta\) must be in radians. Thus, \(r=\frac{s}{\theta}=\frac{12\pi}{3\pi/4}=12\pi\times\frac{4}{3\pi}=16\) cm. Therefore, option C is correct. An error such as choosing 12 cm can result from dividing incorrectly by \(\frac{3\pi}{4}\). 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.
