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.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
Ï€(R2Â Â + r2Â ) = 20020
22/7(R2Â Â + r2Â ) = 20020
(R2Â + r2Â ) = 20020x(7/22)
(R2Â Â + r2Â ) = 6370Â Â Eq.(i)
If the product of the diameters of both circles P and Q is 12348 cm.
2Rx2r = 12348
4Rr = 12348
2Rr = 6174Â Â Eq.(ii)
Sum of the radius of both of the circles = (R+r)
Make a square with the help of a formula.
(R+r)2Â Â = R2Â +r2Â +2Rr
Put Eq.(i) and Eq.(ii) in the above equation.
(R+r)2Â Â = 6370+6174
(R+r)2Â Â = 6370+6174 = 12544
So the sum of the radius of both of the circles = (R+r) = 112 cm
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