A Ferris wheel has a maximum height of 216 feet and a wheel diameter of 200 feet. What is the equation of the...

Question

A Ferris wheel has a maximum height of 216 feet and a wheel diameter of 200 feet. Find an equation for the wheel if the center of the wheel is on the​ y-axis and y represents the height above the ground.

Couldn't fit that in the title. Please help. Its for homework. I don't understand it.

Answer 1

Hi, Bob!

In order to write an equation of the circle, we need two major components: the radius of the circle and the coordinates of its center. We can then express the equation in the form (x - a)² + (y - b)² = r², where r is the radius and (a, b) is the center.

Let's start by first finding the radius of the Ferris wheel. We know that the diameter of the wheel is 200ft, and that the radius of a circle is half of the diameter. So, we have d = 200,

r = d/2

r = 200/2

r = 100ft

Now that we know the radius, we can save that for later and move on to finding the center point.

We are told that the center of the wheel is on the y-axis; this means that the x-coordinate of our center point is a = 0.

Next, to find the y-coordinate, we can note that even though the diameter of the wheel is 200ft, the maximum height of the wheel is actually 216ft. That means that there must be a structure below the wheel that holds it up 16ft above the ground (216 - 200 = 16). Therefore, we must add this 16ft to the radius of 100ft straight up to find the center point of the circle, which is 116ft above the ground. Thus, the y-coordinate of our center point is b = 116.

We can then plug in our radius and center point (0, 116) into our equation for a circle and simplify to get our final answer:

(x - (0))² + (y - (116))² = (100)²

x² + (y - 116)² = 10,000

I hope that this explanation was helpful, and please don't hesitate to reach out if you have any further questions!