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? Give your answer in terms of pi.

Answer 1

now, the bicycle made 3 rotations, namely 3 revolutions, before stopping, one revolution is a full circle, namely 2π radians angle, so 3 times that is 3 * 2π, or 6π.

$\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=14\\ \theta =6\pi \end{cases}\implies s=14\cdot 6\pi$

Answer 2

I assume the question is "how long is the track of water left by the tire?"  The circumference of the tire is the distance around the tire and is equal to:   C = 2·pi·radius C = circumference pi=3.14159 r = radius = 14 inches   The track of water left on the floor by one full rotation of the tire equals one circumference in length.  If the tire rotates 3 full times, the track of water is 3 circumferences long.  Use your calculator to get the answer.