Question

Find the area of a segment of a circle whose radius is 10cm by the corresponding cord subtending 30degree at the center

Answer 1

Here ACB is our required segment . and OA = OB = Radius = r = 10 cm and θ = 30°

In triangle AOB , angle AOB = 30° and OA = OB ( Radius ) and angle AOB is include angle of sides OA and OB

We know area of triangle if given : a , b are the two known sides and " θ " is the included angle . As :

(Diagram is in the attachment)

so,

Area of triangle = a × b × Sin θ / 2 , Here a = b = radius = 10 cm And Angle θ = 30°

Area of minor segment = Area of sector OACB - Area of triangle AOB

Area of minor segment = 30°/360° × 22/7 × 10² × 10 × 10 × Sin 30°/2 × 2 = 1/12 × 2200/7 − (100 × 1/2)/2 = 2200/84 − 50/2 = 26.19 − 25 = 1.19 cm²

and

Area of major segment = Area of circle - Area of minor segment

so,

Area of major segment = 22/7 ×10² − 1.19 = 2200/7 − 1.19 =314.28 − 1.19 = 313.09 cm²

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