Question

The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 132° arc?Give the exact answer in simplest form. ____ square kilometers. (pi, fraction,)

Answer 1

To find the area of the sector we will use

`A=(L\cdot r)/(2)`

Where L is

`\begin{gathered} L=\frac{2\cdot\pi\cdot6\text{ km}}{360^(\circ)}\cdot132^(\circ) \\ L=\frac{132\pi\text{ km}}{30}=\frac{66\pi\text{ km}}{15}=\frac{22\pi\text{ km}}{5} \end{gathered}`

Finally, we must replace L and r in the intial equation