we know that
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=6\ cm[/tex]
Substitute the value of r in the formula
[tex]A=\pi (6^{2})=113.10\ cm^{2}[/tex]
Remember that
The area of [tex]113.10\ cm^{2}[/tex] subtends the complete circle of [tex]360\°[/tex]
so
by proportion
Find the area for the shaded sector of [tex]60\°[/tex]
[tex]\frac{113.10}{360} \frac{cm^{2} }{degrees}=\frac{x}{60} \frac{cm^{2} }{degrees} \\ \\x=60*113.10/360 \\ \\x= 18.85\ cm^{2}[/tex]
therefore
The answer is
The approximate area of the shaded sector is [tex]18.85\ cm^{2}[/tex]
