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?

1 Answer
Jim H
Jul 28, 2015

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

Explanation:

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

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

#theta = s/r#

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

#s = r theta#

In this case::

#s = 18"cm"* (2pi)/3#

# = 6*2pi#cm

# = 12pi#cm

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