Question

in a circle of radius 7 cm is a chord subtends 120 degree at the centre then find the area of the corresponding segment of the circle

Answer 1

Given,
θ = 120
radius = r = 7 cm.
Arearadians = 12r^2(θ – sinθ)
= 1/2 × 49 × (120 – sin120)
= 1/2 × 49 × {120 – 0.5806}
= 1/2 × 49 × 119.4194
= 1/2 × 5851.5506
= 2925.7753

Answer 2

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radius of the circle (r ) = 7 cm

angle subtended by chord at the centre of the circle ( A )

= 120°
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since , we know that ,

area of segment (A in radian)

= 1 /2 ( A - sinA ) × r^2

= 1 / 2 ( 120 - sin120 ) × ( 7 )^2

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in radian,
approximate value of sin120 = 0.5806
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= 1/ 2 ( 120 - 0.5806 ) × 49

= 119.419 × 49 / 2 = 5851.5 / 2

= 2925.7 cm^2 ( approximate )

therefore

area of segment = 2925.7 cm^2

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Your Answer : area = 2925.7 cm^2
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