• anonymous
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.
  • Stacey Warren - Expert
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  • chestercat
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  • anonymous
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 \[\large Area~=~\pi \times r^{2} \times (\frac{\theta}{360})\]

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