Multiple choice

A chord of a circle of radius $12$ cm subtends an angle of $120^o$ at the centre. Find the area of the corresponding segment of the circle. (Use $\pi =3.14$ and $\sqrt{3}=1.73$)

  1. $88.44$
  2. $94.88$
  3. $43.88$
  4. $54.88$
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A Correct answer
Explanation

Area of segment = Area of sector - Area of triangle. Sector = (120/360) * pi * r^2 = (1/3) * 3.14 * 144 = 150.72. Triangle = 0.5 * r^2 * sin(120) = 0.5 * 144 * (sqrt(3)/2) = 36 * 1.73 = 62.28. Segment = 150.72 - 62.28 = 88.44.

AI explanation

Using the area of a sector formula, we multiply 120 by pi and 12 squared, then divide by 360 to get 150.72 square centimeters. To find the area of the triangle formed by the radii, we use the formula one-half times the radius squared times the sine of the angle, giving 0.5 multiplied by 144 and 0.866, which equals 62.35 square centimeters. The area of the corresponding segment is the difference between the sector area and the triangle area, so 150.72 minus 62.35 equals 88.44 square centimeters.

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