Question 1202895: 15. The original "Ferris" wheel, designed by George Washington Gale Ferris Jr., was built for the World's Columbian Exposition of 1893 in Chicago, Illinois. There were 36 fully enclosed gondolas (passenger cars) that carried up to 40 passengers.
This "Ferris" wheel eventually left Chicago and was relocated in St. Louis, Missouri in time for the 1904 Louisiana Purchase Exposition. On May 11, 1906, it was demolished using a dynamite charge and sold for scraps.
The circumference of the "Ferris" wheel had to be large enough to allow for an arc length of 20.64 ft between each gondola. What was the circumference of the original "Ferris" wheel? Round to the nearest whole number.
Found 4 solutions by Theo, greenestamps, ikleyn, Edwin McCravy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The solution from the other tutor is fine (except is is not rounded to the nearest whole number). But his path to the solution is very long....
36 cars, with an arc length of 20.64 feet between cars, means the circumference of the Ferris wheel (treating the cars as points, as must be done to answer the question) is 36*20.64 feet.
ANSWER: 36*20.64 = 743.04 feet, or 743 feet to the nearest whole number.
Answer by ikleyn(52834)  (Show Source):
You can put this solution on YOUR website! .
The original "Ferris" wheel, designed by George Washington Gale Ferris Jr., was built for the World's Columbian Exposition
of 1893 in Chicago, Illinois. There were 36 fully enclosed gondolas (passenger cars) that carried up to 40 passengers.
This "Ferris" wheel eventually left Chicago and was relocated in St. Louis, Missouri in time for the 1904 Louisiana
Purchase Exposition. On May 11, 1906, it was demolished using a dynamite charge and sold for scraps.
The circumference of the "Ferris" wheel had to be large enough to allow for an arc length of 20.64 ft between each gondola.
What was the circumference of the original "Ferris" wheel? Round to the nearest whole number.
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Actually, as it is presented/printed in the post, this problem can not be solved
and the question can not be answered correctly, until the length of each gondola is given.
But it can be, that the goal of a problem composer was to force a reader
to solve the problem, assuming the zero length of gondolas.
If it is so, then I am very shocked to see this solution by @Theo, as long as 14 lines of arguments.
The true solution is much shorter, in one or two lines.
We have 20 arcs, each of 20.64 ft long (along the circumference, as the problem says).
Then the circumference is simply 20*20.64 = 743.04 ft. <<<---=== ANSWER
Solved.
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This "problem" is somewhere between a Math joke and Math stupidity, but closer to Math stupidity.
It contains many words to confuse a reader and to distract his/her attention, but does not contain
vitally important information, which is necessary for solution.
So, the problem's composer not only confuses a reader - - - he/she confuses himself (or herself), too.
I've seen this problem and its duplicates on several other websites.
So, some "thinkers" actively disseminate this gibberish online
instead of throwing it to the trash bin, where its right place should be.
What is strange to me is the fact that other tutors consider this "problem" seriously
and do not see that it is defective.
I have not seen (unfortunately) any qualified tutor expose this problem as invalid.
So, I am first who says "the king is naked".
"The king is naked" refers to "The Emperor's New Clothes," a famous fairy tale by Hans Christian Andersen
about a vain emperor tricked into believing he is wearing invisible, magnificent clothes that are only visible
to the wise. In truth, he is naked, but his courtiers and the townspeople remain silent, afraid of being
thought foolish. The deception is revealed when a child innocently shouts the truth, "The king is naked!".
The story serves as a metaphor for how fear, pride, and conformity prevent people
from speaking truth to power, and how a child's innocence can cut through widespread delusion.
Answer by Edwin McCravy(20060)  (Show Source):
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