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Question

AC and BD are two perpendicular diameters of a circle ABCD. It is given that the area of the shaded portion is 308 cm2. The circumference of the circle is
241945_b9d5d611e57a4816873f0bb972782533.png

A
44 cm
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B
66cm
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C
88cm
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D
77cm
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Solution

The correct option is C 88cm

GivenAB&CDaretwoprpendicularlybisectingdiametersofacirclewithcenterO.ar.AOB+ar.COD=308cm2.


TofindoutThecircumference=C=?


SolutionLettheradiusofthecircle=r.AB&CDaretwoprpendicularlybisectingdiametersofthecircle.


SoAOB=90o=CODandOA=OB=OC=OD(radiiofthesamecircle).AOB&CODaretwoequalsectorswithcentral


angleθ=90oandradius=r.


Soar.sectorAOB=ar.sectorCOD


i.ear.sectorAOB+ar.sectorCOD=2×ar.sectorAOB.


Nowarsector=θ360o×π×r2whenθisthecentralangle


andristheradiusofthesector.


Hereθ=90o.


bythegivencondition,


2×ar.sectorAOB=308


2×90o360o×227×r2=308


r2=308×2×722cm2r=14cm


C=2πr=2×227×14cm=88cm.


AnsOptionC.



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