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The sum of the areas of two circles is 130 ft^2.the difference of the areas is 112 ft^2. What the radius of each circle.

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4 Answers

pi r_1^2 + pi r_2^2 = 130 ft^2
 
pi r_1^2 - pi r_2^2 =112 ft^2
 
Add the equations:
 
2 pi r_1^2 = 242
 
pi r_1^2 = 121 => r_1 = sqrt(121/pi) = 11/sqrt(pi) feet, exactly
 
Using calculator with built-in pi value:
r_1 ≈ 6.20608541902532 feet, approximately
 
121 + pi r_2^2 = 130
 
pi r_2^2 = 130 - 121 = 9
 
r_2 = sqrt(9/pi) = 3/sqrt(pi) feet, exactly
 
Using calculator with built-in pi value:
r_2 ≈ 1.69256875064327 feet, approximately
Hi Willie,Let radius of ist circle is r1 & radius of 2nd circle is r2.
Area of first circle =  Pie *r1^2
Area of 2nd circle = pie*r2^2
Now sum of areas of two circles=pie(r1^2+r2^2)=130.....Eq-1
       Diff of areas=pie(r1^2 -r2^2)=112........Eq-2
adding Eq-1 & Eq-2, We get,2pie*r1^2=242                              ( value of pie = 22/7)
                                       
                                         2*22/7*r1^2=242
                                r1^2=242*7/2*22= 38.5
                                            r1= sq root of 38.5=6.2ft
Now substituting the value of r1^2 inti Eq-1,
                      pie(r1^2+r2^2)=130
                       22/7(38.5+r2^2)=130
                           38.5+r2^2=130*7/22
                             r2^2=41.36-38.5=2.86
                             r2= sq root of 2.86=1.7ft
Ans: radius of one circle is 6.2ft & radius 2nd circle is 1.7ft.
 
Meena from Strongsville,OH
 
 
 ∏ r1^2 + ∏r2^2 = 130 ft2
∏ r1^2  -  ∏r2^2  = 112 ft^2
 
   r1^2 + r2 ^ 2  = 130 /∏ =41.4
   r1^2  - r2 ^ 2  =  112/ ∏=35.7
     2 r1^2 = 77.1
 
      r1 ^ 2 = 38.6
 
      r1 = √38.6 = 6.2 ft
 
       r2 ^ 2 = 44.4 - 35.7 = 8.7
 
        r2 = √8.7 = 2.9 ft
    
 
Radius of ince cirlce - R1 and other circle - R2
Area of a circle = pi x R2
 
As per question
 
(pi x R12) + ( pi x R22) = 130
 
(pi x R12) - (pi x R22) = 112
 
=> R12 + R22 = 130/pi         equation 1
     R12 - R22 = 112/pi           equation 2
=>  R12 = 112/pi   + R22  Substitute this value of R12 in equation 1
=> 112/pi  + R22 + R22 = 130/pi
=> 2 R22 = 130/pi - 112/pi = 18/pi
=>  R22 = 18/2pi = 9/pi
=> R2 = √(9/pi) = 3/√pi = 3/1.77 = 1.69 ft
 
Substitute this value of R2 in equation 2
R12 - 9/pi = 112/pi
R12 = 112/pi + 9/pi = 121/pi
R1 = √(121/pi) = 11/√pi = 6.21 ft