Answer:
The length of the arc is [tex]27\pi \ cm[/tex]
Step-by-step explanation:
step 1
Find the circumference
we know that
The length of a complete circle is equal to the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=18\ cm[/tex]
substitute
[tex]C=2\pi (18)[/tex]
[tex]C=36\pi\ cm[/tex]
step 2
we know that
A central angle of [tex]2\pi[/tex] radians subtends the circumference of [tex]36\pi\ cm[/tex]
so
by proportion
Find the length of the arc by a central angle of [tex]\frac{3\pi }{2}[/tex] radians
[tex]\frac{36\pi }{2\pi}\frac{cm}{radians}=\frac{x}{(3\pi/2)}\frac{cm}{radians} \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm[/tex]
