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Three concentric circles are drawn such that the area of the smallest circle is equal to the area of each of the rings. If the radius of the largest circle is 12 cm, what is the radius of the smallest circle?

 Feb 11, 2018
 #1
avatar+96055 
+1

Call S  the radius of the smallest circle  and  M the radius of the intermediate circle

 

pi (12)^2  -  pi (M)^2  =  pi ( S)^2     (1)       and

 

pi (M)^2  - pi(S)^2   = pi (S)^2    ⇒  pi (M)^2  = 2 pi (S)^2   (2)

 

Sub (2)  into  (1)

 

pi (12)^2  - 2pi(S)^2  = pi (S)^2

 

12^2  - 2S^2 + S^2

 

12^2   =  3S^2

 

144  = 3S^2

 

48 = S^2

 

√48  = S

 

4√3  cm  = S   ≈  6.93 cm

 

 

cool cool cool

 Feb 11, 2018

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