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
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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