+0  
 
0
112
2
avatar+157 

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?

AdminMod2  Aug 18, 2017

Best Answer 

 #1
avatar+5205 
+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?

 

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

hectictar  Aug 18, 2017
Sort: 

2+0 Answers

 #1
avatar+5205 
+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+78575 
+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

CPhill  Aug 18, 2017

6 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details