Multiple choice

The radius of a circle is 14 cm. If angle subtended by an arc of a circle at centre is $45^{\circ}$, then length of arc is

  1. $44\ cm$
  2. $11\ cm$
  3. $56\ cm$
  4. $28\ cm$
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B Correct answer
Explanation

Arc length = (theta/360) * 2 * pi * r = (45/360) * 2 * (22/7) * 14 = (1/8) * 88 = 11 cm.

AI explanation

The length of an arc is calculated using the formula l = (theta/360) * 2 * pi * r. Substituting the given radius of 14 cm and the angle of 45 degrees into the formula gives l = (45/360) * 2 * pi * 14. Simplifying the fraction 45/360 to 1/8 results in l = (1/8) * 28 * pi. Therefore, the arc length is 11 cm using the approximation pi = 22/7.

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