Question

A Ferris wheel is an amusement park ride comprised of a large wheel rotating on an axis. There are cars or compartments where people can sit or stand that are evenly spaced about the circumference of the circle. The wheel rotates slowly, taking passengers on a ride around the circumference of the circle.
Please select one of the following famous Ferris wheels to research:
• Singapore Flyer
• London Eye
• Star of Nanchang
You will need to find the diameter and number of compartments (or cars) for the one you chose in order to be able to complete the calculations section of the assignment. Once you have your information, move on to step 2.

Complete the following tasks and calculations. You must show all work and steps to receive full credit.
1. Name of the Ferris wheel
London Eye
2. Diameter of the wheel (in meters)
324
3. Number of cars or compartments

4. Circumference of the wheel (in meters)
C = 2(60)(3.14)
C = 120*3.14
C = 276.8
5. Area of the wheel (in meters)

6. Measure of a central angle in degrees
Supposing that the capsules are equally spaced, it would be 360/32, which is 11.25. Measure of a central angle in radians: 0.2054083
7. Measure of a central angle in radians

8. Arc length between two cars or compartments
Arc between two capsules: 11.775 meters
9. Area of a sector between two cars or compartments
Area of a sector between two capsules: 0.19625
Answer the following questions. You must show all steps and provide any evidence needed in your solution to receive full credit.
10. If a smaller replica of the Ferris wheel was constructed, what conclusions could you draw about the central angle of the original wheel and replica? What conclusions could you draw about the arc length of the original Ferris wheel and replica?
The central angle would be similar because angles don’t change when dilated. But the arc of the replica would change because the radius is changed.
11. Imagine the center of the Ferris wheel is located at (0, 0) on a coordinate grid, and the radius lies on the x-axis. Write an equation of a circle for your Ferris wheel, and sketch an image of what your Ferris wheel would look like on the grid. Now graph a circle that is similar to the Ferris Wheel. Discuss the transformations needed to show that both circles on your graph are similar.
(x-0)2 + (y - 0)2 = 60^2

Answer 1

@AZ

Answer 2

wth am i looking at...

Answer 3

It looks like everything is already answered, are you just checking your work or something?

Answer 4

I only answered some parts but for the most part it isn't answered

Answer 5

Looking at number 6, it looks like it's 36 spaces, so 36 compartments for number 3

Answer 6

When you search it up it says 32

Answer 7

Oh sorry, I looked wrong, yes, 32

Answer 8

And the for number 5, area should be easy, it's just pi times r^2

Answer 9

For number 7, you already wrote it in number 6

Answer 10

Oh whoops wrong place, thanks for pointing that out

Answer 11

I'm not sure of the meaning of the last one, when you draw it.... the center would be at the origin point already, what does it mean by the transformations

Answer 12

I.. have no idea

Answer 13

Well, I think that what you wrote is correct, since that's how you would write it out in desmos or something to get the graph

Answer 14

Ah, splendid

Answer 15

Although, maybe change the 60^2 to 3600

Answer 16

Ok thank you

Answer 17

yw~

Answer 18

For #2, you said that the diameter is 324 m

That would mean that the radius is 182 m

So I'm confused why you plugged in r = 60 in the circumference formula for #4

But I just googled and I see that it's actually 394 feet and 120 meters so never mind. You'd just want to correct #2 then

Answer 19

#8 and 9, I'm not sure how you got those values

arc length = \(\dfrac{\theta}{360^o}\times 2 \pi r\)

or just radius * the angle in radians

and speaking of which, while #6 is correct- #7 is slightly off

to go from degrees to radians, you have to multiply by pi/180


but never mind, I guess you're just using 3.14 instead of the entire pi value but even then I don't know huh

Answer 20

11.25 * pi/180 = 0.19635 radians

your #8 is very close so I'll assume it's most likely some rounding error but #9 is very off

Area of a sector = 1/2 * r^2 * angle in radians

Answer 21

For #11, they just want to you to create a similar circle with the same radius but just do some transformations

so you've written it as
(x + 0)^2 + (y + 0)^2 = 60^2

which can really be written as x^2 + y^2 = 60^2

keep in mind that the circle equation is
(x-h)^2 + (y-k)^2 = r^2

so (h, k) would be the center of the circle

so you can just choose another center for a new similar triangle that has a radius of 60

Answer 22

So what is 8 and 9?

Answer 23

so #7 should be 0.19635 radians like I said

#8 would be
arc = radius * angle in radians

arc = 60 * 0.19635

#9 would be
sector area = 1/2 * r*2 * angle in radians

sector area = 1/2 * 60^2 * 0.19635

Answer 24

all you had to do was plug in the numbers and solve it

Answer 25

Ok thank you I'll try that now

Answer 26

No problem