Multiple choice

The area of a segment of a circle of radius $21 cm$, if the arc of the segment has a measure of $\displaystyle 60^{\circ}$ is: (Take $\sqrt{3}=1.73 $)

  1. $\displaystyle 45.27\:cm^{2}$
  2. $\displaystyle 40.27\:cm^{2}$
  3. $\displaystyle 40.8\:cm^{2}$

  4. None of the above
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B Correct answer
Explanation

Area of segment = Area of sector - Area of triangle. Sector area = (60/360) * pi * 21^2 = (1/6) * (22/7) * 441 = 231. Triangle area = (sqrt(3)/4) * 21^2 = 0.4325 * 441 = 190.73. Segment area = 231 - 190.73 = 40.27.

AI explanation

The area of the segment is found by subtracting the area of the triangle from the area of the sector. Using the sector area formula, 60 degrees divided by 360 degrees multiplied by pi and 21 squared, gives 231 square centimeters. Using the equilateral triangle area formula, the area is root 3 divided by 4 multiplied by 21 squared, which is 441 times 1.73 divided by 4, resulting in approximately 190.73 square centimeters. Subtracting the triangle area from the sector area gives 231 minus 190.73, which equals 40.27 square centimeters.

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