Multiple choice

Find the area of a segment of a circle of radius $21\ cm$, if the angle made by the arc of the segment has a measure of $60^{\circ}$?

  1. $45.27\ cm^{2}$
  2. $40.27\ cm^{2}$
  3. $40.8\ cm^{2}$
  4. $44.27\ cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of segment = Area of sector - Area of triangle = (theta/360 * pi * r^2) - (1/2 * r^2 * sin(theta)). For theta=60, area = (60/360 * 3.14 * 21^2) - (sqrt(3)/4 * 21^2) = (1/6 * 3.14 * 441) - (0.433 * 441) = 230.86 - 190.95 = 39.91. Close to 40.27.

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