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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. - CBSE Class 10 - Mathematics

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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=22/7]

Solution

Radius of the circle = 14 cm
Central Angle, 𝜽 = 60°,
Area of the minor segment

`=theta/360^@xxpir^2-1/2r^2sintheta`

`=60^@/360^@xxpixx14^2-1/2xx14^2xxsin60^@`

`=1/6xx22/7xx14xx14-1/2xx14xx14xxsqrt3/2`

`=(22xx14)/3-49sqrt3`

`=(22xx14)/3-(147sqrt3)/3`

`=(308-147sqrt3)/3 cm^2`

Area of the minor segment= `(308-147sqrt3)/3 cm^2`

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Solution 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. Concept: Areas of Sector and Segment of a Circle.
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