Multiple choice

The circumference of a circle is $100$ cm. The length of an arc of central angle $90$ is

  1. $25$ cm
  2. $50$ cm
  3. $75$ cm

  4. none of these
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A Correct answer
Explanation

The circumference of a circle corresponds to an angle of 360 degrees. An arc with a central angle of 90 degrees is 90/360 = 1/4 of the total circumference. Thus, the arc length is 100/4 = 25 cm.

AI explanation

The fraction of the circle represented by a 90 degree central angle is 90 / 360, which reduces to 1 / 4. The length of the corresponding arc is this same fraction of the total circumference of 100 cm. Multiplying 100 cm by 1 / 4 gives an arc length of 25 cm.

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