Given a figure of a circle:
As shown, the radius of the circle = r = 9 miles
The shown sector bounded by a 60-degree arc
We need to find the area of the shown sector
as we know the area of the circle =
[tex]\pi\cdot r^2[/tex]
The area of the sector represents 60/360 of the area of the circle
So, the area of the sector =
[tex]\frac{60}{360}\cdot\pi\cdot r^2=\frac{1}{6}\cdot3.1416\cdot9^2=42.4115[/tex]
so, the answer will be the area of the shown sector = 42.4115 square miles
We will write the area in terms of pi and fractions as follow:
[tex]\frac{1}{6}\cdot\pi\cdot9^2=\frac{27}{2}\pi[/tex]
So, the answer will be:
[tex]\frac{27}{2}\pi[/tex]
