A person riding the original Ferris Wheel is traveling at a speed of 0.495 mph. If one revolution takes 9 minutes, what is the diameter of the Ferris Wheel? Show your work.
1 rev is distance of pi D
so pi D feet/9 minutes = speed in feet/min
.495 mi/h * 5280 ft/mi * 1 h/60 min
= 43.56 feet/min
SO
pi D/9 = 43.56
D = 9 (43.56)/pi
or
D = 125 feet
To find the diameter of the Ferris Wheel, we need to first calculate the circumference of the wheel and then use that information to find the diameter.
The circumference of a circle can be calculated using the formula:
Circumference = π * Diameter
Given that one revolution of the Ferris Wheel takes 9 minutes and the speed of the person on the wheel is 0.495 mph, we can determine the distance traveled in one revolution.
The distance traveled in one revolution can be calculated by multiplying the speed (0.495 mph) by the time it takes (9 minutes). However, since the speed is given in mph and the time is in minutes, we should convert the speed to mph before calculating the distance.
To convert mph to miles per minute, we divide the speed by 60 (as there are 60 minutes in an hour):
0.495 mph / 60 = 0.00825 miles per minute.
Now we can calculate the distance traveled in one revolution:
Distance = Speed * Time
Distance = 0.00825 miles per minute * 9 minutes
Distance = 0.07425 miles
Since we know that the distance traveled in one revolution is equal to the circumference of the Ferris Wheel, we can find the diameter by using the formula for the circumference of a circle.
Circumference = π * Diameter
Now we rearrange the formula to solve for Diameter:
Diameter = Circumference / π
Substituting the known values:
Diameter = 0.07425 miles / π
To find the diameter, we need to use the value of π. The value of π is approximately 3.14159.
Diameter = 0.07425 miles / 3.14159
Diameter ≈ 0.0236 miles
So, the diameter of the Ferris Wheel is approximately 0.0236 miles.