Multiple choice

The length of an arc subtending an angle of measure $60^0$ at the centre of a circle whose area is $616\ cm^2$ is........

  1. $\dfrac { 22 }{ 3 } $
  2. $66$
  3. $\dfrac { 44 }{ 3 } $
  4. $33$
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C Correct answer
Explanation

Area = pi*r^2 = 616. r^2 = 616 * 7/22 = 28 * 7 = 196. r = 14. Arc length = (theta/360) * 2 * pi * r = (60/360) * 2 * (22/7) * 14 = 1/6 * 2 * 22 * 2 = 88/6 = 44/3.

AI explanation

The area of a circle is pi * r^2, so 616 = (22/7) * r^2, which gives r^2 = 196 and r = 14 cm. The length of an arc is calculated using the formula (theta / 360) * 2 * pi * r. Substituting the values gives (60 / 360) * 2 * (22/7) * 14, which simplifies to (1/6) * 88 = 44/3 cm.

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