Multiple choice

A chord AB of a circle of radius 5.25 cm makes an angle of 60° at the centre of the circle. Find the area of the major and minor segments. (Take π = 3.14)

  1. 168 cm2

  2. 42 cm2

  3. 84 cm2

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of the circle is pi * r^2 = 3.14 * 5.25^2 = 86.55 square centimeters. The area of the minor segment is calculated as the area of the 60-degree sector minus the area of the equilateral triangle OAB, which gives approximately 2.49 square centimeters. Subtracting this from the total area of the circle yields the area of the major segment as approximately 84.06 square centimeters, which matches option C.

AI explanation

The area of the sector is 14.43 square cm and the area of the triangle is 11.95 square cm, yielding a minor segment area of about 2.48 square cm. The total circle area is 86.55 square cm, so the major segment area is 86.55 minus 2.48, which is 84.07 square cm. The result is 84 cm2.

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