Question

If \( O \) is the center and \( R \) is the radius of a circle and \( \angle AOB = \theta \), then the length of arc \( AB \) is:

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

Hint:

Use the formula \( L = \frac{\theta}{360^\circ} \times 2 \pi R \) to find the length of an arc when the central angle and radius are known.

Answer 1

The Correct Option is B

The length of an arc is given by the formula: \[ L = \frac{\theta}{360^\circ} \times 2 \pi R, \] where \( \theta \) is the central angle and \( R \) is the radius of the circle. Thus, the length of the arc \( AB \) is \( \boxed{\frac{2 \pi R \theta}{360}} \).