Question

A hamster wheel has a radius of 4 and 1/2 in. How far will the wheels turn in one revolution

Answer 1

one revolution, namely one go-around the circle, is an angle of 2π radians, in radians unit of course.

now, we know the radius is 4 and 1/2 long, so, what is the "arc" made by the 2π radians angle, with that radius?


`\bf \textit{arc's length}\\\\ s=r\theta \qquad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ \theta =2\pi \\ r=4(1)/(2)=(9)/(2) \end{cases}\implies s=\cfrac{9}{2}\cdot 2\pi \implies s=9\pi`