Multiple choice

Find the difference of the areas of two segments of a circle formed by a chord of length $5\ cm$ . Subtending an angle of $90^{o}$ till the centre.

  1. $32.14$ sq. cm
  2. $35.42$ sq. cm
  3. $38.96$ sq. cm
  4. $42.43$ sq. cm
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A Correct answer
Explanation

Area of segment = Area of sector - Area of triangle. Sector angle = 90 degrees. Area of sector = (90/360) * pi * r^2. Chord length = 5, so r^2 + r^2 = 5^2 => 2r^2 = 25 => r^2 = 12.5. Area of sector = 0.25 * 3.14 * 12.5 = 9.8125. Area of triangle = 0.5 * r^2 = 6.25. Area of segment = 9.8125 - 6.25 = 3.5625. The difference between the two segments is (pi * r^2 - 3.5625) - 3.5625 = 39.25 - 7.125 = 32.125.

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