Rotation of a cirle with the diameter of 34"

Question

The diameter of the rear tire of this bike is 34". In low gear, you need to rotate the pedals 3x to make the rear tire rotate 360 degrees. How far will you travel in low gear each time you rotate the pedals?

Answer 1

"rotate the pedals 3x to make the rear tire rotate 360 degrees"   means 

      rotate the pedals 1x to make the rear tire rotate 120 degrees    [that is, (1/3)*360°]

 

So, what is (1/3) of the circumference of a circle with diameter 34"?

 

The definition of π (pi) is the ratio of the circumference of a circle to its diameter  (π = C/d).  So, C = πd.

 

And,

  (1/3)C = (1/3)(π)(34")

             = 35.6"

 

To check (or approximate):

     Since Pi is a little more than 3 and the diameter is 34", then the bicycle will travel approximately (a little more than) 34" with one rotation of the pedals.