Chapter 11.6, Problem 2WE

To determine

To Find: The arc length and area of each sector.

Answer to Problem 2WE

Arc length: $\pi$

Area: $2\pi sq.units$

Explanation of Solution

Given: $\angle AOB=45,r=4$

Given: $\angle AOB=45,r=4$

  

Arc length

  $\begin{array}{l}=\frac{x}{360}(2\pi r)\\ =\frac{45}{360}(2\pi (4))\\ =\pi \end{array}$

Area of the shaded sector.

  $\begin{array}{l}=\frac{x}{360}(\pi r^2)\\ $ =\frac{45}{360}(\pi {(4)}^2)$=\frac{1}{8}(16\pi )\\ =2\pi sq.units\end{array}$