Question

A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit.

Answer 1

Well what I'm thinking is that if there are 20 cars, they should be evenly spaced about. So it's just asking for the angle, arc length, and area for each 1/20th of the circle. The way to find the central angle between 2 cars is the \[\large \frac{Total~Angle~of~a~circle}{no.~of~cars}~=~\theta\] The arc length can be found using the formula \[\large Arc~=~2\pi r \times (\frac{\theta}{360})\] Area of a car can be found using the formula \[\large Area~=~\pi \times r^{2} \times (\frac{\theta}{360})\]