Given−AB&CDaretwoprpendicularlybisectingdiametersofacirclewithcenterO.ar.AOB+ar.COD=308cm2.
Tofindout−Thecircumference=C=?
Solution−Lettheradiusofthecircle=r.AB&CDaretwoprpendicularlybisectingdiametersofthecircle.
So∠AOB=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=308×2×722cm2⇒r=14cm
∴C=2πr=2×227×14cm=88cm.
Ans−OptionC.