Question

What is the arc length and then I need to know the area sector

Answer 1

1. 6.28 inches

2. 9.42 square inches

Step-by-step explanation:

From the diagram:

• The central angle subtending arc AB = 120 degrees.

,

• The radius of the circle, r=3 inches.

Part A (Arc Length)

`\text{Length of an arc=}(\theta)/(360\degree)*2\pi r`

Substituting the central angle and radius, we have:

`\begin{gathered} \text{Length of an arc=}(120\degree)/(360\degree)*2*\pi*3 \\ =(1)/(3)*6\pi \\ =2\pi\text{ inches } \\ =6.28\text{ inches (to 2 decimal places)} \end{gathered}`

Part B (Area of the Sector)

`\text{Area of a }\sec tor\text{=}(\theta)/(360\degree)*\pi r^2`

Substituting the central angle and radius, we have:

`\begin{gathered} \text{Length of an arc=}(120\degree)/(360\degree)*\pi*3^2 \\ =(1)/(3)*9\pi \\ =3\pi\text{ square inches } \\ =9.42\text{ square inches (to 2 decimal places)} \end{gathered}`