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# pls help lol

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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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#1
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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°

CPhill  Sep 11, 2017
#2
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Thanks a lot!

Guest Sep 12, 2017

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