SOLUTION: The front wheel of a child's tricycle has a 10-inch radius and the rear wheels have a 6-inch radius. The pedals are attached to the front wheels by arms that are 7 inches long. How
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-> SOLUTION: The front wheel of a child's tricycle has a 10-inch radius and the rear wheels have a 6-inch radius. The pedals are attached to the front wheels by arms that are 7 inches long. How
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Question 966857: The front wheel of a child's tricycle has a 10-inch radius and the rear wheels have a 6-inch radius. The pedals are attached to the front wheels by arms that are 7 inches long. How far does a pedal travel when the rear wheels make one revolution? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the front wheel has a radius of 10 inches.
the front pedal has a radius of 7 inches.
the rear wheel has a radius of 6 inches.
one revolution of the rear wheel is exactly equal to the circumference of the rear wheel.
this is equal to 2 * pi * 6 which is equal to 12 * pi.
the circumference of the pedal is equal to 2 * pi * 7 which is equal to 14 * pi.
the pedal will actually be traveling the same distance as the rear wheel.
however, that same distance represents 12 * pi / 14 * pi = 6/7 of the circumference of the pedal.
the rear wheel will have traveled 360 degrees.
the pedal will have traveled 6/7 * 360 = 308.5714286 degrees.
the formula to calculate the arc length of 308.5714286 degrees is:
arc length = 308.5714286 / 360 * 2 * pi * 7 which is equal to 12 * pi.
that's the same distance of travel as the rear wheels did in one complete revolution.
