Question

A restaurant on the top of a building is shaped like a circle with a radius of 80 feet. The restaurant rotate 60 degrees every 15 minutes. Two diners notice a bird that is sitting on a ledge outside of a window. If the bird stays on the ledge outside of a window, approximately how far will the bird travel in an hour?

Answer 1

Since, the restaurant rotates 60° every 15 minutes, then it will rotate 60°*4=240°

in one hour.

The full rotation of the restaurant is represented by 360°

Then,

$\begin{gathered} \text{Circunference}=2\pi r \\ 2\pi r=2\pi\cdot80=160\pi \end{gathered}$

Having the length of the circunference, we know that 240° is only 2/3 from the full rotation, so the bird will travel in one hour:

$160\pi\cdot\frac{2}{3}=335.1\text{ ft}$