Question 1202895
there were 36 fully enclosed gondolas.
360 degrees divided by 36 = 10 degrees central angles between each gondola.
the length of the arc between each gondola is given as 20.64 feet.
you get 10/360 * 2 * pi * r = 20.64
that's the formula for the length of the arc which is then used to find the radius of the ferris wheel.
multiply both sides of this equation by 360 to get 10 * 2 * pi * r = 20.64 * 360.
simplify to get 20 * pi * r = 7430.4
divide both sides of the equation by (20 * pi) to get r = 7430.4 / (20 * pi) = 118.2584889 feet.
that's the radius of the sphere.
the circumference of the ferris wheel is equal to 2 * pi * 118.2584889 = 743.04 feet.
since there are 36 arcs, the distance between each arc is 743.04 / 36 = 20.64 feet.
that's the arc length between each gondola.
the numbers check out and so the solution appears to be reasonably correct.
the solution is that circumference of the original ferris wheel was 743.04 feet.