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A sector of a circle is shown below.  The sector has an area of $60 \pi.$  What is the radius of the circle?

 

 Dec 17, 2023
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A sector of a circle is shown below.  The sector has an area of $60 \pi.$  What is the radius of the circle?  

 

I'm not sure what \pi means.  Does the backslant mean divided by pi, or is the backslant just another one of those useless symbols like all those dollar signs in every problem I look at.  I don't know about you, but I would use a forward slant to mean divided by.  I'm going to treat the backslant as meaningless.  

 

The shaded area is a fourth of the circle, indicated by the right angle in the center. 

 

                                                          Acircle  

                                                        –––––––  =  60 π  

                                                             4  

 

                                                           A  =  240 π  

 

                                                           A  =  π r2   

 

therefore                                       240 π  =  π r2     

 

                                                            r2  =  240  

 

                                                            r  =  sqrt(240)  

 

                                                            r  =  4 • sqrt(15)  

.

 Dec 18, 2023

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