Question

NEED HELP ASAP!!!!!

A restaurant on the top of a building is shaped like a circle with a radius of 80 feet. the restaurant rotates 60 degrees every 15 minutes. two diners notice a bird that is sitting on a ledge outside of a window. one diner argues that the bird will travel 160 feet in an hour since the diameter of the restaurant is 160 ft while the other diner argues that the bird will travel a longer distance. If the bird stays on the ledge outside of the window approximately how far will the bird travel in one hour?
A. 213 ft
B. 335 ft
C. 377 ft
D. 503 ft

Answer 1

If restaurant rotates
`60^(0)` every 15 minutes, then after one hour it will rotate
`60^(0)*4=240^(0)`.
When restaurant makes full rotation
`360^(0)`, the length will be
`2 \pi r=2 \pi *80=160\pi`. But
`240^(0)` is only
`(2)/(3)` from the full rotation, so the bird will pass
`160\pi * (2)/(3) =335` ft

Answer: B is a correct choice