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Question

PQRS is the diameter of a circle of radius 3 cm. The lengths PQ, QR and RS are equal. Find the area of the shaded portion

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A
2πcm2
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B
5π2cm2
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C
9π2cm2
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D
11π2cm2
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Solution

The correct option is B 5π2cm2
GiventhatthesemicirclewithdiameterPShasaradiusr1=3cm.PS=3×2cm=6cm.AlsoPQ=QR=RS.PQ=QR=RS=63cm=2cm.Soar.semicircleofdia.PSi.eradiusr1=3cmis12×π×r12=12×π×32cm2=92×πcm2.AgainthesemicirclewithdiameterQShasaradiusr2=12(QR+RS)=12(2+2)cm=2cm.Soar.semicircleofdia.QSi.eradiusr2=2cmis12×π×r22=12×π×22cm2=2πcm2.Nowar.shadedportion=ar.semicircleofdia.PSar.semicircleofdia.QS=92×πcm22πcm2=5π2cm2.Ansar.shadedportion=5π2cm2.

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