Answer:
α = 12°
L = 6.28 ft
[tex]A = 94.25 ft^2[/tex]
Step-by-step explanation:
The wheel contains 30 cars attached to it.
The wheel is in the shape of a circle and a circle has 360°.
Therefore, the angle between any two cars will be:
360 / 30 = 12°
The length of the arc between two cars is given as:
[tex]L = \frac{\alpha }{360} * 2\pi R[/tex]
where α = central angle of sector
R = radius of circle
Given that the radius of the wheel is 30 feet, the length of the arc is:
[tex]L = \frac{12}{360} * 2 * \pi * 30\\\\L = 6.28 ft[/tex]
The area of a sector is given by:
[tex]A = \frac{\alpha }{360} * \pi R^2[/tex]
Therefore, the area of the sector between any two cars is:
[tex]A = \frac{12}{360} * \pi * 30^2\\\\A = 94.25 ft^2[/tex]
