Math, asked by gulbadansah0gmailcom, 14 days ago

Find the difference of the areas of two segments of a circle formed by a chord of length 7 cm subtending an angle of 60 at the centre.​

Answers

Answered by amitnrw
0

Given : a chord of length 7 cm subtending an angle of 60 degree at the center​

To Find :  difference of the areas of two segments of a circle formed by   chord

Solution:

a chord of length 7 cm subtending an angle of 60 degree at the center

Hence chord will form am equilateral triangle with center

so radius of circle =  7 cm

Area of smaller segment = Area of sector with 60° angle - area of triangle

= (60/360)π(7)² -  (√3 / 4)7²

= 49 ( π/6 -  √3 / 4)

360° - 60° = 300°

Area of larger segment = Area of sector with 300° angle + area of triangle

= (300/360)π(7)² +  (√3 / 4)7²

= 49 ( 5π/6 + √3 / 4)

the difference of the areas of two segments of a circle

= 49 ( 5π/6 + √3 / 4) - 49 ( π/6 -  √3 / 4)

= 49 ( 4π/6 + 2√3 / 4)

=  49 ( 2π/3 +  √3 / 2)

= 49 * 2.96

≈  145 cm²

Difference of the areas of two segments of a circle formed by  chord is 145 cm²

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