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The perimeter of a sector of a circle with central angle 90° is 25cm. The area of the minor segment of the circle is

Posted by Rimi Das 3 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sumit Yadav 3 years, 10 months ago

Let r be the radius of the circle and θ be the angle. Now, Perimeter of the sector=(2r+2πrθ360) =2r+2×227×r×90360=(2r+11r7)=25r7 Also, 25r7=25⇒r=(25×725)⇒r=7 cm Area of the minor segment=(πr2θ360−12r)2sin θ cm2 =∣∣(227×7×7×90360)−(12×7×7×sin 90°)∣∣ cm2=(772−492) cm2=282 cm2=14 cm2

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