How do you find the length of an arc of a circle with a radius of 18cm if the arc subtends a central angle of 2(pi) / 3?

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How do you find the length of an arc of a circle with a radius of 18cm if the arc subtends a central angle of 2(pi) / 3?

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Answer 1 · 2015-07-28T12:40:30

The arc has length $12 π$ $12pi$ cm. (About $37.7$ $37.7$ cm.)

Explanation:

The radian measure of an angle, $θ$ $theta$ can be defined by:

Let $θ$ $theta$ be a central angle in a circle of radius $r$ $r$ . Let $s$ $s$ be the length of the arc cut off by $θ$ $theta$ . Then the radian measure os $θ$ $theta$ is given by:

$θ = \frac{s}{r}$ $theta = s/r$

Thus if we are given radius and the central angle in radians, we can find the arc length using:

$s = r θ$ $s = r theta$

In this case::

$s = 18 cm \cdot \frac{2 π}{3}$ $s = 18"cm"* (2pi)/3$

$= 6 \cdot 2 π$ $= 6*2pi$ cm

$= 12 π$ $= 12pi$ cm

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How do you find the length of an arc of a circle with a radius of 18cm if the arc subtends a central angle of 2(pi) / 3?

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