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In the figure, the visible gray area within the larger circle is equal to eight times the area of the white circular region. What is the ratio of the radius of the small circle to the radius of the large circle? Express your answer as a common fraction.

 

 Jun 18, 2021
 #1
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Since   we can position the white  circle  anywhere in the  gray area, let  the  circles  be concentric

 

Area  of  larger circle =   pi*r^2  + 8pir^2  =  9pi r^2     where r is the  radius of the  smaller  circle

 

So

 

Ratio   of areas  =

 

  pi r^2

_______     =    1/9

9 pi r^2

 

The  ratio  of  the  radii  =   sqrt  (1/9) =   1 / 3

 

 

cool cool cool

 Jun 18, 2021
edited by CPhill  Jun 18, 2021

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