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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.

 

 Apr 19, 2021

Best Answer 

 #1
avatar+31353 
+2

larger circle - smaller circle   =   8 * smaller circle      area

 

pi L2   -    pi S2              =    8 pi  S2  

L^2 - S^2  = 8 S^2

L^2 = 9 S^2  

S/L = 1/3

 Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021
 #1
avatar+31353 
+2
Best Answer

larger circle - smaller circle   =   8 * smaller circle      area

 

pi L2   -    pi S2              =    8 pi  S2  

L^2 - S^2  = 8 S^2

L^2 = 9 S^2  

S/L = 1/3

ElectricPavlov Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021

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