How do you find the radius of a circle given the length of an arc?

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How do you find the radius of a circle given the length of an arc?

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Answer 1 · 2015-11-29T20:58:10

The circle with radius $r$ $r$ has a circumference $2 \cdot π \cdot r$ $2*pi*r$ which corresponds to an angle of $360^{o}$ $360^o$ .

If you are given an arc of a certain angle lets say $p^{o}$ $p^o$ degrees which is $l$ $l$ in length then

$\frac{p^{o}}{360^{o}} = \frac{l}{2 \cdot π \cdot r} \Rightarrow r = \frac{360^{o} \cdot l}{2 \cdot π \cdot p^{o}}$ $p^o/360^o=l/(2*pi*r)=>r=(360^o*l)/(2*pi*p^o)$

Answer 2 · 2016-09-02T09:40:14

$r = \frac{180 \times l}{π θ}$ $r = (180 xxl)/( pi theta)$

Explanation:

You always need another piece of information, just the arc length is not enough - the circle could be big or small and the arc length does not indicate this.

It will help to be given the sector angle.

If you have the sector angle $θ$ $theta$ , and the arc length, $l$ $l$ then you can find the radius

$r = \frac{180 \times l}{π θ}$ $r = (180 xxl)/(pi theta)$

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How do you find the radius of a circle given the length of an arc?

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