Question

The circle has center O. Its radius is 2 m, and the central angle a measures 70°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer

Answer 1

We have the following:

We can calculate the shaded area of a circle is the following

$\begin{gathered} a=\frac{\pi\cdot r^2\cdot\theta}{2\pi} \\ r=2 \\ \theta=70=70\cdot\frac{\pi}{180}=\frac{7}{18}\pi \end{gathered}$

replacing:

$\begin{gathered} a=\frac{\pi\cdot2^2\cdot\frac{7}{18}\pi}{2\pi} \\ a=\frac{7}{9}\pi \end{gathered}$

The area is 7/9 pi m^2