Question

Find the length of an arc of 40° in a circle with an 8 inch radius

Answer 1

Radians: $s = \theta r$
               $s = \frac{s}{r}(r)$
               $s = \frac{40}{8}(8)$
               $s = 5(8)$
               $s = 40\°$
               $s = \frac{4\pi}{18}$

Degrees: $s = \theta\frac{\pi}{180}r$
                $s = \frac{s\pi}{180r}(r)$
                $s = \frac{40\pi}{180(8)}(8)$
                $s = \frac{40\pi}{180}$
                $s = \frac{4\pi}{18}$
                $s = 40\°$

Arc Length = $\frac{\theta}{360\°} * C$
Arc Length = $\frac{5\°}{360\°} * 2\pi r$
Arc Length = $\frac{1}{72} * 2(3.14)(8)$
Arc Length = $\frac{1}{72} * 2(25.12)$
Arc Length = $\frac{1}{72}(50.24)$
Arc Length ≈ $0.698131701$