Answer:
[tex]\displaystyle \frac{2\pi}{5}[/tex] inches.
Step-by-step explanation:
What is the circumference of this circle? The question states that radius [tex]r = 2[/tex] inches.
[tex]C = \pi \cdot d = 2 \pi \cdot r = 4 \pi[/tex].
A full circle is similar to a sector of [tex]360^{\circ}[/tex]. The [tex]36^{\circ}[/tex] sector here will be a [tex]\displaystyle \frac{36^{\circ}}{360^{\circ}} = \frac{1}{10}[/tex] slice of the entire circle. Its arc length will be equal to [tex]\displaystyle \frac{1}{10}[/tex] the circumference of the full circle. That's
[tex]\displaystyle \frac{4 \pi}{10} = \frac{2\pi}{5}[/tex] inches.
