Answer:
the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]
Step-by-step explanation:
Use the fraction of the area of the circle associated with the red sector. Use a proportion to find the appropriate fraction knowing that a full circle [tex](360^o)[/tex] corresponds to the area:
[tex]Area=\pi\,R^2=\pi\, (8\,in)^2= 64\, \pi\,\,in^2[/tex]
then the proportion goes like:
[tex]\frac{64\,\pi\,\,in^2}{360^o} =\frac{sector}{165^o} \\ sector=\frac{64\,\pi\,165^o}{360^o}\,\,in^2\\sector\approx 92.15\,\,in^2[/tex]
Therefore, the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]
