Area of the circle
The are of a circle is given by:
[tex]A(\text{circle) = }\pi\cdot r^2[/tex]
Where:
π = 3.14159
r = radius of the circle
In our problem we have:
r = 5
So, applying the formula of above we find that:
[tex]A(\text{circle) = }\pi\cdot5^2\cong78.5398\cong78.5[/tex]
Circle Area = 78.5 mi²
Area of the sector area of the circle
We can calculate the area of a sector of a circle using the following formula:
[tex]A(\text{sector) = }\pi\cdot r^2\cdot\frac{\theta}{360}[/tex]
Where:
θ = angle of the sector
In our problem we have:
θ = 60°
So, applying the formula of above we find that:
[tex]A(\text{sector) = }\pi\cdot5^2\cdot\frac{60}{360}\cong13.0899\cong13.1[/tex]
Sector Area = 13.1 mi²
