If arc \(s=11\pi\) cm and angle \( \theta=\frac{\pi}{2} \) radians, what is the radius?
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Answer and explanation
Correct answer: 22 cm
When the angle is in radians, the arc-length formula is \(s=r\theta\). Thus, \(r=\frac{s}{\theta}=\frac{11\pi}{\pi/2}=11\pi\times\frac{2}{\pi}=22\) cm. The option \(22\pi\) cm is incorrect because the \(\pi\) terms cancel. Exam tip: Use this formula directly only when the angle is measured in radians.
Frequently asked questions
What is the correct answer to this question?
22 cm
Why is this the correct answer?
When the angle is in radians, the arc-length formula is \(s=r\theta\). Thus, \(r=\frac{s}{\theta}=\frac{11\pi}{\pi/2}=11\pi\times\frac{2}{\pi}=22\) cm. The option \(22\pi\) cm is incorrect because the \(\pi\) terms cancel. Exam tip: Use this formula directly only when the angle is measured in radians.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
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