How long is the trace of water left on the floor?

Question

A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 14 inches, and the bicycle wheel makes 3 full rotations before stopping. How long is the trace of water left on the floor?

Answer 1

We want to find the distance covered in three fill wheel rotations given that the radius is 14 inches. If we were to do one full wheel rotation, that is the same as saying going around the entire circle once, or the circumference of the circle.

 

The circumference can be calculated by using the relation between radius and circumference

 

circumference = 2 * pi * radius

 

Given that your radius is 14 inches, we can plug this right in

 

circumference = 2 * pi * 14 inches = 28 * pi inches

 

This is for one wheel rotation. For three rotations, simply multiply the result by three.

 

3 full rotations = trace of water = 3 * circumference = 3 * 28 * pi inches = 84 * pi inches