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Question

The perimeter of a sector of a circle with central angle 90° is 25 cm. The area of the minor segment of the circle is
(a) 14 cm2
(b) 16 cm2
(c) 18 cm2
(d) 24 cm2

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Solution

(a) 14 cm2
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=25r=25×725r=7 cm
Area of the minor segment=πr2θ360-12r2sin θ cm2
=227×7×7×90360-12×7×7×sin 90° cm2=772-492 cm2=282 cm2=14 cm2

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