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a sector has area of 15.3 square meters. the radius of the circle is 3 meters.

a. find the radian measure of the central angle

b. find the degree measure of the central angle

c. find the arc length of the sector. 

Guest Mar 9, 2018
 #1
avatar+90968 
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Area of sector  =  (1/2)r^2 * (theta in rads )

 

So

 

15.3  = (1/2) (3)^2 *  ( theta in rads)

 

15.3   =  9/2   * (theta in rads )       multiply both sides  by  2/9

 

15.3 (2/9)  =  (theta in rads)

 

3.4   =   theta  in rads

 

 

To  conert this to degrees  we have

 

3.4    *  180° / pi   ≈  194.8°

 

To  find the arc length, S,     we have

 

S    =  2 * pi  (radius)   (194.8 / 360)  =

 

2 * pi * 3  *  (194.8 / 360)  =  

 

6* ( 194. 8 / 360)  * pi   ≈   81.26 m

 

 

cool cool cool

CPhill  Mar 9, 2018

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