<h3>Answers:</h3>
- Central angle = 18 degrees
- Arc length = 7.85 feet approximately
- Area of sector = 98.17 square feet approximately
All of these answers apply to just between two adjacent or neighboring cars. For the last two answers, I used the calculator's stored value of pi instead of something like pi = 3.14
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Explanation:
A full circle is 360 degrees. Divide this into 20 equal pieces to get 360/20 = 18. Each little pie slice is 18 degrees. This is the central angle between any two adjacent or neighboring cars.
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The circumference of the ferris wheel is 2*pi*r = 2*pi*25 = 50pi feet exactly. This is the total distance around the circle. We only want a small portion of that. Namely, we want the curved distance from one car to its neighbor. Go for the shortest distance possible.
The formula we'll use is
L = (x/360)*2*pi*r
note how 2*pi*r is the circumference of the circle, so we're taking a fractional portion (x/360) of this full circle perimeter to get the arc length L. The value of x is the central angle.
So,
L = (x/360)*2*pi*r
L = (18/360)*2*pi*25
L = (1/20)*50pi
L = (50/20)pi
L = 2.5pi
L = 7.85398163397449 feet
L = 7.85 feet approximately
I used my calculators stored version of pi, as opposed to something like pi = 3.14
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The last part of this problem is finding the area of the sector between two neighboring cars. The full circle has area of pi*r^2 = pi*25^2 = 625pi square feet exactly.
We'll take a fraction of this, specifically 1/20 th of the area, to get the pie slice area we want
area of sector = (1/20)*(area of circle)
area of sector = (1/20)*625pi
area of sector = 31.25pi
area of sector = 98.174770424681 approximately
area of sector = 98.17 square feet approximately
