What is the perimeter of a sector with radius (10) cm and angle \(\frac{2\pi}{5}\)?
Answer and explanation
Correct answer: \(20+4\pi\) cm
The perimeter of a sector is the sum of its two radii and its arc length: \(P=2r+r\theta\), where \(\theta\) is in radians. Here, the arc length is \(10\times\frac{2\pi}{5}=4\pi\) cm. Therefore, \(P=2(10)+4\pi=20+4\pi\) cm. Option C incorrectly takes the arc length as \(2\pi\). Exam tip: when the angle is in radians, use \(r\theta\) directly for arc length.
Frequently asked questions
What is the correct answer to this question?
\(20+4\pi\) cm
Why is this the correct answer?
The perimeter of a sector is the sum of its two radii and its arc length: \(P=2r+r\theta\), where \(\theta\) is in radians. Here, the arc length is \(10\times\frac{2\pi}{5}=4\pi\) cm. Therefore, \(P=2(10)+4\pi=20+4\pi\) cm. Option C incorrectly takes the arc length as \(2\pi\). Exam tip: when the angle is in radians, use \(r\theta\) directly for arc length.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
