We have been given that Circle C has diameter AE with a length of 2 cm, and a central angle with the measure [tex]40^{\circ}[/tex]. We are asked to find the length of arc DE.
We will use arc length formula to solve our given problem.
[tex]l=\frac{\theta}{180}\times \pi r[/tex], where,
[tex]l[/tex] = Arc length,
[tex]\theta[/tex] = Central angle in degrees.
r = radius of circle.
Since AE is diameter, so radius will be half of AE.
[tex]r=\frac{2\text{ cm}}{2}=1\text{ cm}[/tex]
[tex]l=\frac{40}{180}\times 3.14 \times (1\text{ cm})[/tex]
[tex]l=\frac{2}{9}\times 3.14 \times (1\text{ cm})[/tex]
[tex]l=0.697777\text{ cm}[/tex]
Upon rounding to nearest tenth, we will get:
[tex]l\approx 0.7\text{ cm}[/tex]
Therefore, the length of arc DE is approximately 0.7 cm.
