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Which one represents the area of a sector?

 Jan 30, 2020
 #1
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+1

 

We suspect that it's the first one, so let's explore the possibility. 

 

Let's try to figure it out logically. Okay, pi r squared is the area of an entire circle.     

 

Now it might not be good to start with an angle like, oh, 77o for instance.  Hard to visualize.      

 

Pick an angle that's obvious, easy to visualize.  So, why don't we pick 180o to start with.    

 

We know that 180o represents half a circle, and 180/360 = 1/2 so that works out good.   

 

Try 90o next.  That's obviously a fourth of a circle, and 90/360 = 1/4 so I think we can be confident. 

 

It's definitely the first one.      

 Jan 30, 2020
 #2
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 1)     A = n / 360° pi * r²              A = 90° / 360° * pi * 5²             A ≈  19.635 u²  

 

Number 2 works for   r = 1          A = n / 360° * pi * r         A = 90° / 360° * pi * 1        A ≈ 0.785 u°    

 

A = 360 / 360 * pi * 5²            A ≈ 78.539 u²         indecision

 Jan 30, 2020

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