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The length of an arc of a circle is $12$ cm. The corresponding sector area is $108$ cm$^2$. Find the radius of the circle.

I have not attempted this question and do not understand how to solve this.

Andrea
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Ziyaan janmohamed
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  • @Ziyaan. First question one should ask: What are the formulas for the circumference and area of a circle? – imranfat Jan 19 '16 at 15:24
  • Welcome to Math SE. Please note that this is not really where you get other people to do your homework. Try to attempt your problem, in any way, and say what confuses you. In this case you could use the above advice, or try to draw a picture to start with. – Andrea Jan 19 '16 at 15:28

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If $\theta$ is the central angle in radians and $r$ is the radius, we can write the two following equations: $r\theta = 12$ and $\frac{1}{2}\theta r^{2} = 108.$ Dividing the first equation into the second, we have that $\frac{1}{2}r = 9,$ so $\boxed{r = 18}.$

K. Jiang
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