Question

Find the arc length of a central angle of 36° in a circle whose radius is 2 inches,

Answer 1

`\displaystyle (2\pi)/(5)` inches.

Explanation:

What is the circumference of this circle? The question states that radius
`r = 2` inches.

`C = \pi \cdot d = 2 \pi \cdot r = 4 \pi`.

A full circle is similar to a sector of
`360^(\circ)`. The
`36^(\circ)` sector here will be a
`\displaystyle (36^(\circ))/(360^(\circ)) = (1)/(10)` slice of the entire circle. Its arc length will be equal to
`\displaystyle (1)/(10)` the circumference of the full circle. That's

`\displaystyle (4 \pi)/(10) = (2\pi)/(5)` inches.