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The larger circle has center O and passes through D. The smaller circle has diameter OD. What percent of the larger circle's area is gray?

 Aug 18, 2017

Best Answer 

 #1
avatar+7352 
+3
gray circle area =

π

* (radius)2    
                                radius of the smaller circle  =  \(\frac{OD}{2}\)
gray circle area =

π

* (\(\frac{OD}{2}\))2    
             
gray circle area =

π

* \(\frac{OD^2}{4}\)    
             
gray circle area =

\(\frac{πOD^2}{4}\)

   

 

 

larger circle area =

π

* (radius)2    
                              radius of the larger circle  =  OD
larger circle area =

π

* OD2    

 

 

What, percent, is the gray circle's area out of the larger circle's area?

 

\(\frac{\text{gray circle area}}{\text{larger circle area}}\,=\,\frac{\frac{\pi OD^2}{4}}{\pi OD^2}\,=\,\frac{\pi OD^2}{4}\,*\,\frac{1}{\pi OD^2}\,=\,\frac14\,=\,\frac{25}{100}\,=\,25\%\)

.
 Aug 18, 2017
 #1
avatar+7352 
+3
Best Answer
gray circle area =

π

* (radius)2    
                                radius of the smaller circle  =  \(\frac{OD}{2}\)
gray circle area =

π

* (\(\frac{OD}{2}\))2    
             
gray circle area =

π

* \(\frac{OD^2}{4}\)    
             
gray circle area =

\(\frac{πOD^2}{4}\)

   

 

 

larger circle area =

π

* (radius)2    
                              radius of the larger circle  =  OD
larger circle area =

π

* OD2    

 

 

What, percent, is the gray circle's area out of the larger circle's area?

 

\(\frac{\text{gray circle area}}{\text{larger circle area}}\,=\,\frac{\frac{\pi OD^2}{4}}{\pi OD^2}\,=\,\frac{\pi OD^2}{4}\,*\,\frac{1}{\pi OD^2}\,=\,\frac14\,=\,\frac{25}{100}\,=\,25\%\)

hectictar Aug 18, 2017
 #2
avatar+98197 
+2

 

Thanks, hectictar......!!!!

 

Another thing to realize is that circles are to one another as the squares of their radiuses.....

 

Thus.....the smaller circle has a radius of 1/2 the larger circle...so...its area  = (1/2)^2  = 1/4  that of the larger circle

 

 

cool cool cool

 Aug 18, 2017

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