Answer:
1. 6.28 inches
2. 9.42 square inches
Explanation:
From the diagram:
• The central angle subtending arc AB = 120 degrees.
,
• The radius of the circle, r=3 inches.
Part A (Arc Length)
[tex]\text{Length of an arc=}\frac{\theta}{360\degree}\times2\pi r[/tex]
Substituting the central angle and radius, we have:
[tex]\begin{gathered} \text{Length of an arc=}\frac{120\degree}{360\degree}\times2\times\pi\times3 \\ =\frac{1}{3}\times6\pi \\ =2\pi\text{ inches } \\ =6.28\text{ inches (to 2 decimal places)} \end{gathered}[/tex]
Part B (Area of the Sector)
[tex]\text{Area of a }\sec tor\text{=}\frac{\theta}{360\degree}\times\pi r^2[/tex]
Substituting the central angle and radius, we have:
[tex]\begin{gathered} \text{Length of an arc=}\frac{120\degree}{360\degree}\times\pi\times3^2 \\ =\frac{1}{3}\times9\pi \\ =3\pi\text{ square inches } \\ =9.42\text{ square inches (to 2 decimal places)} \end{gathered}[/tex]
