The area of a circular sector with radius r and a central angle θ (in degrees) is given by the formula:
[tex]A=\pi r^2\cdot\frac{\theta}{360}[/tex]
Substitute r=15ft and θ=145 to find the area covered by the sprinkler:
[tex]\begin{gathered} A=\pi\cdot(15ft)^2\cdot\frac{145}{360} \\ =\frac{725}{8}\pi\cdot ft^2 \\ =284.71\ldots ft^2 \\ \approx285ft^2 \end{gathered}[/tex]
If the radius of the sector is 12 feet, then the area would be:
[tex]\begin{gathered} A=\pi\cdot(12ft)^2\cdot\frac{145}{360} \\ =\frac{4176}{73}\pi\cdot ft^2 \\ =179.72\ldots ft^2 \\ \approx180ft^2 \end{gathered}[/tex]
