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In a​ circle, a 135degrees sector has area 54pi in2. What is the radius of the​ circle?

 May 12, 2020
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We  have  that  135°  =  (3/4)pi  rads

 

The area  of the  sector has the form

 

A =  (1/2) r^2 ( theta in rads)

 

So

 

54 pi  =  (1/2) r^2 [ 3/4] pi       divide out pi

 

54  = (1/2) (3/4) r^2

 

54  = (3/8) r^2        divide both sides by 3

 

18  = (1/8) r^2     multiply both sides by 8

 

144 = r^2       take the positive  root

 

12 (in)  = r

 

 

cool cool cool

 May 12, 2020

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