Multiple choice

In a circle of radius 21 cm, an arc subtends an angle of $60^{\circ}$ at the centre. The area of the segment formed by the corresponding chord of the arc is :

  1. 42 $cm^2$
  2. 421.73 $cm^2$
  3. 429.43 $cm^2$
  4. 40 $cm^2$
Reveal answer Fill a bubble to check yourself
D 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 = (1.732/4) * 441 = 190.95. Segment area = 231 - 190.95 = 40.05. Option D is the closest.

AI explanation

The area of the segment is the difference between the area of the sector and the area of the triangle. The area of the sector with a central angle of 60 degrees is (60/360) * (22/7) * 21^2 = 231 sq cm. The area of the equilateral triangle formed by the radii and the chord is (sqrt(3)/4) * 21^2 = 441 * sqrt(3) / 4, which is approximately 190.96 sq cm. The area of the segment is 231 - 190.96 = 40.04 sq cm, which rounds to 40 sq cm.

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