Multiple choice

If an arc of a circle subtends an angle of $ \displaystyle x^{\circ} $ at the centre then the length of the arc will be equal to - (Given radius of the circle=r)

  1. $ \displaystyle \frac{x}{360}(2\pi r) $
  2. $ \displaystyle \frac{360}{x}(2\pi r) $
  3. $ \displaystyle \frac{x}{360}\left ( \frac{1}{2\pi r} \right ) $

  4. None of these
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A Correct answer
Explanation

The length of an arc is a fraction of the circumference. The fraction is the angle x divided by the total degrees in a circle (360). Thus, Arc length = (x/360) * (2 * pi * r).

AI explanation

The total angle at the centre of a circle is 360 degrees, making the total circumference 2 times pi times r. The fraction of the angle subtended by the arc is x divided by 360. Therefore, the length of the arc is the fraction x divided by 360 multiplied by the total circumference of 2 times pi times r.

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