Answer:
the answer is the option B
[tex]138\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=12\ cm[/tex]
substitute
[tex]A=\pi (12)^{2}=144\pi\ cm^{2}[/tex]
Remember that
[tex]360\°[/tex] subtends the complete circle of area [tex]144\pi\ cm^{2}[/tex]
so
by proportion
find the area of the shaded sector for a central angle of [tex]110\°[/tex]
[tex]\frac{144\pi }{360} \frac{cm^{2}}{degrees} =\frac{x}{110} \frac{cm^{2}}{degrees} \\ \\x=144\pi *110/360\\ \\x= 138.23\ cm^{2}[/tex]
Round to the nearest square centimeter
[tex]x= 138\ cm^{2}[/tex]
