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=(1)/(2)r^2\theta \\ \text{Here r =2in is the radius,} \\ \theta=(40)/(180)*\pi=0.223\pi \\ \text{Now,} \\ A=(1)/(2)*2^2*0.223\pi \\ A=0.446\pi\text{ in\textasciicircum{}2} \end{gathered}`