A bicycle wheel has a diameter of 2 feet and turns at the rate of 70 revolutions per minute. How fast does the wheel move in feet per hour?
One rotation is π(diameter) = 2π ft
so in one minute it goes 70(2π) = 140π) ft
in one hour it goes 60(140π) ft
= 8400π ft/hr
or appr 26389 ft/hr
To find out how fast the wheel moves in feet per hour, we first need to determine the distance traveled by the wheel in one revolution.
The circumference of a circle is given by the formula C = π * d, where C is the circumference and d is the diameter.
In this case, the diameter of the bicycle wheel is 2 feet. Plugging this value into the formula, we get:
C = π * 2 = 2π feet
Therefore, the wheel travels a distance of 2π feet in one revolution.
Next, we need to determine the distance traveled by the wheel in one minute. We know that the wheel makes 70 revolutions per minute, so:
Distance traveled in one minute = (2π feet/revolution) * 70 revolutions = 140π feet
Now we need to convert this into feet per hour. Since there are 60 minutes in an hour, we simply multiply the distance traveled in one minute by 60:
Distance traveled in one hour = (140π feet/minute) * 60 minutes = 8400π feet
Approximately, the value of π is 3.14, so we can calculate the final answer:
Distance traveled in one hour ≈ 8400 * 3.14 feet = 26,376 feet
Therefore, the wheel moves at a speed of approximately 26,376 feet per hour.