Answer:
The arc length is [tex]2\pi[/tex] inches or 6.28 inches
Step-by-step explanation:
To solve this we are using the arc length formula:
[tex]s=r\alpha[/tex]
where
[tex]s[/tex] is the arc length
[tex]r[/tex] is the radius of the circle
[tex]\alpha[/tex] is the central angle in radians
We know from our problem that the central angle is [tex]\frac{\pi }{4}[/tex] and the radius of the circle is 8 inches, so [tex]\alpha =\frac{\pi }{4}[/tex] and [tex]r=8in[/tex]. Let's replace the values to find [tex]s[/tex]:
[tex]s=r\alpha[/tex]
[tex]s=(8in)(\frac{\pi }{4} )[/tex]
[tex]s=2\pi in[/tex]
[tex]s=6.28in[/tex]
