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The length of an arc of a circle is 12cm. The corresponding sector area is 108cm2.

Find: 

  • The radius of the circle
  • The angle subtended at the centre of the circle by the arc.
Guest Sep 11, 2017
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2+0 Answers

 #1
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+1

 

Arc length, S,  =  r * θ           wher r is the radius and θ  is  in radians

 

Area of a sector  =   (1/2) (r^2)*θ

 

So........

 

12  = r * θ      → θ  =   12 / r    (1)

 

And

 

108 =  (1/2) (r^2) * θ         subbing (1)  into this, we have that

 

108 = (1/2) (r^2) * (12 /r)        simplify

 

216  = 12 r         divide both sides by 12

 

18  = r  = the radius

 

And to find the angle subtended by the arc  is given by    θ  =   12 / r    →  θ  =   12 / 18  =  2 / 3

 

And this is in rads......so  to convert to degrees we have   .....     (2/3)  *  180° / pi  ≈  38.19°  

 

 

 

cool cool cool

CPhill  Sep 11, 2017
 #2
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Thanks a lot!

Guest Sep 12, 2017

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