If A Bicycle Wheel Has A Diameter Of 27 Inches, Find The Radian Measure Of The Angle Through Which The Wheel Turns As The Bicycle Travels A Distance Of 1 Mile
Circumference = pi*Dia. = 3.14 * 27 = 84.823 in = 7.07 Ft.
1 Mile = 5,280 Ft.
5,280Ft. * 6.28rad/7.07Ft. = 4,690 Rad.
To find the radian measure of the angle through which the wheel turns, we need to use the formula:
θ = distance traveled / radius
First, let's convert the given distance of 1 mile into inches. There are 5280 feet in a mile and 12 inches in a foot, so 1 mile is equal to 5280 * 12 = 63,360 inches.
Next, we need to find the radius of the bicycle wheel.
The diameter is given as 27 inches. The radius is half of the diameter, so the radius would be 27 / 2 = 13.5 inches.
Now we can calculate the radian measure of the angle by plugging in the values into the formula:
θ = 63,360 inches / 13.5 inches
Simplifying the calculation, we get:
θ = 4688.89 radians
Therefore, the radian measure of the angle through which the wheel turns as the bicycle travels a distance of 1 mile is approximately 4688.89 radians.