Central angle (in green): As the wheel has 20 cars divide 360º into 20 to find the central angle:
[tex]\alpha=\frac{360º}{20}=18º[/tex]Arc length (in blue):
[tex]\begin{gathered} Al=\frac{\alpha}{360º}\cdot2\pi r \\ \\ Al=\frac{18º}{360º}\cdot2\pi\cdot25ft \\ \\ Al=\frac{1}{20}\cdot2\pi\cdot25ft \\ \\ Al=\frac{50}{20}\pi ft \\ \\ Al=\frac{5}{2}\pi ft \\ \\ Al=7.85ft \end{gathered}[/tex]Area of the sector:
[tex]\begin{gathered} As=\frac{\alpha}{360º}\cdot\pi\cdot r^2 \\ \\ As=\frac{18º}{360º}\cdot\pi\cdot(25ft)^2 \\ \\ As=\frac{1}{20}\cdot\pi\cdot625ft^2 \\ \\ As=\frac{625}{20}\pi ft^2 \\ \\ As=98.17ft^2 \end{gathered}[/tex]Then, the central angle is 18º, the arc length is 7.85 feet and the area of a sector is 98.17 square feet
