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

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What have you tried? –  Ron Gordon Mar 18 '13 at 16:32
Do you know a formula for the area of a sector? –  Ross Millikan Mar 18 '13 at 16:35

1 Answer 1

It is natural to let $r$ be the radius of the circle, and $\theta$ the angle of the sector, preferably measured in radians.

The length of the arc is then $r\theta$. The area of the sector is $\frac{1}{2}r^2\theta$. Again, writing down these two facts is natural, since we are given the arc length and area.

We know $r\theta$, and also know $\frac{1}{2}r^2\theta$. From this it should not be difficult to find $r$. A simple way is to note that $\frac{r^2\theta}{r\theta}=r$.

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thanks for your answer. –  Scholar 95 Mar 18 '13 at 16:57
You are welcome. I take it you had no trouble with the numerical computation part. –  André Nicolas Mar 18 '13 at 16:59

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