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Question

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60.Also find the area of the corresponding major segment. [Use π=227]
 


Solution

Let ACB be the given arc subtending an angle of 60 at the centre.

θ=60 and OA = OB.
OAB is an equilateral triangle.

Here,r= 14 cm and θ=60.
Area of the minor segment ACBA=(Area of the sector OACBO)-(Area of OAB)

=πr2θ36034r2

=227×14×14×60360  34×14×14


=3083493

=17.79 cm2

Area of the major segment BDAB=Area of circle-Area of minor segment ACBA

=πr217.89

=227×14×1417.89

= 616 - 17.89

= 598.11=598 cm2.
 

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