Multiple choice

An arc of circle subtends an angle of $ \displaystyle 30^{\circ} $ at the centre If the radius of the circle is 7 cm then length of the arc will be equal to -

  1. $ \displaystyle 3\frac{1}{3} cm $
  2. $ \displaystyle 3\frac{1}{2} cm $
  3. $ \displaystyle 3\frac{2}{3} cm $

  4. None of these
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C Correct answer
Explanation

Arc length = (theta/360) * 2 * pi * r. Arc length = (30/360) * 2 * (22/7) * 7 = (1/12) * 44 = 44/12 = 11/3 = 3 and 2/3 cm.

AI explanation

The length of an arc is calculated using the formula (central angle divided by 360) multiplied by 2, pi, and the radius. Substituting the given values gives (30 divided by 360) multiplied by 2, (22 divided by 7), and 7. This simplifies to one-twelfth of 44, which is 11 divided by 3. The result is 3 and two-thirds cm.

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