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    Question

    The sum of the areas of two circles P and Q is 20020 cm2. If the product of the diameters of both circles P and Q is 12348 cm, then find out the sum of the radius of both of the circles.

    A 112 cm Correct Answer Incorrect Answer
    B 128 cm Correct Answer Incorrect Answer
    C 96 cm Correct Answer Incorrect Answer
    D 104 cm Correct Answer Incorrect Answer
    E None of the above Correct Answer Incorrect Answer

    Solution

    Let’s assume the radius of circles P and Q are ‘R’ and ‘r’.

    The sum of the areas of two circles P and Q is 20020 cm2.

    πxR2 + πxr2  = 20020

    π(R2  + r2 ) = 20020

    22/7(R2  + r2 ) = 20020

    (R2 + r2 ) = 20020x(7/22)

    (R2  + r2 ) = 6370    Eq.(i)

    If the product of the diameters of both circles P and Q is 12348 cm.

    2Rx2r = 12348

    4Rr = 12348

    2Rr = 6174    Eq.(ii)

    Sum of the radius of both of the circles = (R+r)

    Make a square with the help of a formula.

    (R+r)2  = R2 +r2 +2Rr

    Put Eq.(i) and Eq.(ii) in the above equation.

    (R+r)2  = 6370+6174

    (R+r)2  = 6370+6174 = 12544

    So the sum of the radius of both of the circles = (R+r) = 112 cm

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