Question

The circle has center O. Its radius is 2 in, and the central angle a measures 40°. What is the area of the shaded region? Give the exact answer in terms of pi, and be sure to include the correct unit

Answer 1

$\begin{gathered} \text{The formula for the sector of circle is as follows:} \\ A=\frac{1}{2}r^2\theta \\ \text{Here r =2in is the radius,} \\ \theta=\frac{40}{180}\times\pi=0.223\pi \\ \text{Now,} \\ A=\frac{1}{2}\times2^2\times0.223\pi \\ A=0.446\pi\text{ in\textasciicircum{}2} \end{gathered}$