The measure of central angle θ (in radian) that cuts from a given circle both an arc of length of 14∏ metres & a corresponding sector of area 168∏ metres square ?

dear shashank ,

total  area of circle = A

 for 2pi rad area = A

for 1 rad area = A/2pi

for θ radian area = Aθ/2pi     =   R²θ/2  ............1                ( A = piR² )

arc/radius =  θ

arc = θR          ............2

area = R² θ = 168pi      .......3                   (given)

arc = R θ = 14pi           .......4                     (given)

 solving  3 & 4  we get

 θ = 7pi/12               ans

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