Question

If \(O\) is the centre and \(r\) is the radius of a circle and \(\angle AOB=\theta\) (in degrees), then the length of arc \(AB\) is equal to:

• A. \(\dfrac{\pi r^{2}\theta}{180}\)
• B. \(\dfrac{\pi r \theta}{360}\)
• C. \(\dfrac{\pi r \theta}{180}\)
• D. \(\dfrac{\pi r^{2}\theta}{360}\)

Hint:

For angles in degrees, arc length \(s=\dfrac{\theta}{360}\times 2\pi r\). For angles in radians, \(s=r\theta\).

Answer 1

The Correct Option is C

Step 1: Use the arc length formula for central angle in degrees.
Length of arc \(s\) corresponding to central angle \(\theta^\circ\) is \[ s=\frac{\theta}{360^\circ}\times 2\pi r. \]
Step 2: Simplify the expression.
\[ s=\frac{\theta}{360}\cdot 2\pi r=\frac{\pi r \theta}{180}. \]
Step 3: Conclude.
Hence, the length of arc \(AB\) is \(\dfrac{\pi r \theta}{180}\).