Answer:
The length of the arc shown in red is [tex]\frac{22}{9}\pi\ in[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=4\ in[/tex]
substitute
[tex]C=2\pi (4)[/tex]
[tex]C=8\pi\ in[/tex]
step 2
Find the length of the arc in red
Remember that the length of the circumference subtends a central angle of 360 degrees
so
by proportion find the length of the arc by a central angle of 110 degrees
[tex]\frac{8\pi}{360}=\frac{x}{110}\\ \\x=8\pi*110/360\\ \\x=\frac{880}{360}\pi\ in[/tex]
Simplify
[tex]\frac{880}{360}\pi=\frac{22}{9}\pi\ in[/tex]
