Question

a chord AB of a circle with centre o subtracted an angle of 120degrees at the centre if the radius of the circle is 30 cm find the area of the minor sector APB
$( \sqrt{3 } \: = \: 1.7 \: \pi \: = \: 3.14)$

Answer 1

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Answer 2

Radius = 30cm
Area of Circle
=πr^2
=3.14*30*30
=2826cm^2
Angle of sector=120°
Angle of sector within circle=120°/360°=1/3
Therefore, area of sector =1/3*area of Circle
=1/3*2826
=942cm^2
If we draw an imaginary parallelogram AOBC,
Then, area of triangle=1/2bh
=30*30/2
=30*15
=450cm^2
Then,area of segment APB =area of sector-area of triangle
=942-450
=492cm^2

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