Question

The tire of a car has a radius of 11.5 inches. How many revolutions does the tire need to make for the

to travel 13,200 inches?

Answer 1

`\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=11.5 \end{cases}\implies C=2\pi (11.5)\implies C=23\pi`

now, that's the circumference, or namely another way to say that's the car's arc length or a revolution.

now, how many times does 23π go into 13200?
`\cfrac{13200}{23\pi }~~ \approx ~~ \stackrel{revolutions}{182.68}`