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In the figure, the visible gray area within the larger circle is equal to \(8\) 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.

 

 Jan 10, 2022
 #1
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x = white area

 

larger circle area =   8x + x = 9 x

 

small circle area = pi r1= x

Larger circle       = pi r22   = 9x  =   9 pi r1 2

 

pi r12  /  9 pi r12   =    1/ 9

 Jan 10, 2022
 #2
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**** correction ****

 

x = white area

 

larger circle area =   8x + x = 9 x

 

small circle area = pi r12  = x

Larger circle       = pi r22   = 9x  =   9 pi r12

 

   r22 = 9 r12

  r1 / r2  =  sqrt ( 1/9) ]  =    1/3

Guest Jan 10, 2022
 #3
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Geometry is defined as “a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.” * Put simply, geometry is a type of math that deals with points, lines, shapes, and surfaces.

 

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 Jan 11, 2022

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