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a sector AOB of a circle with centre O and radius r cm . the angle AOB is θ radians. the area of the sector is 12cm^2 . the perimeter of the sector is 4 times the length of the arc AB

 

find the value of r

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 Aug 15, 2019
 #1
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Area of  sector  =   (1/2) r^2 * θ

 

12 = (1/2) r^2 * θ

 

24 = r^2 * θ

 

The perimeter of the  sector   =   2r  +  arc length of AB

 

4 arclength AB   = 2r + arclength AB

 

3arclength of  AB  = 2r         divide both  sides by 3

 

arclength of AB   =  (2/3)r

 

And  the arclength of  AB  =  r * θ

 

So

 

r * θ   = (2/3)r    (  divide out  r )  ⇒   θ  = (2/3) rads

 

So

 

24  = r^2 * (2/3)

 

24 (3/2)  = r^2

 

72 / 2  = r^2   

 

36  = r^2      take the  square  root  of  both  sides

 

6 (cm)   = r 

 

 

cool cool cool

 Aug 15, 2019
edited by CPhill  Aug 15, 2019

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