Multiple choice

In a circle having radius r, an arc of a circle subtends an angle $\theta$ at the centre, then the length of arc l = ...............

  1. $\dfrac{\pi r^2 \theta}{360}$
  2. $\pi r^2$
  3. $2 \pi r$
  4. $\dfrac{\pi r \theta}{180}$
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D Correct answer
Explanation

The length of an arc is given by (theta / 360) * 2 * pi * r. This simplifies to (theta * pi * r) / 180.

AI explanation

The length of an arc is calculated using the formula l equals pi multiplied by r multiplied by theta, divided by 180. By substituting the radius r and the central angle theta into this formula, we get l equals the fraction pi r theta over 180. The result is pi r theta over 180.

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