Answer:
[tex]27.9cm^2[/tex]
Step-by-step explanation:
The total area of the circle is given by:
[tex]a=\pi r^2[/tex]
where [tex]\pi[/tex] is a constant [tex]\pi=3.1416[/tex]
and [tex]r[/tex] is the radius: [tex]r=8cm[/tex]
Thus the total area of this circle is:
[tex]a=(3.1416)(8cm)^2\\a=(3.1416)(64cm^2)\\a=201.06cm^2[/tex]
We want only the area of the arc that measures 50°. For this we must remember that the arc of the total circle is 360°.
Thus, we want 50° out of the 360° degrees in the circle. For this, we divide the total area by 360 and then we multiply by 50:
[tex]\frac{201.06cm^2}{360}(50)=0.5585cm^2(50)=27.9cm^2[/tex]
the area of the sector to the nearest tenth is [tex]27.9cm^2[/tex]
