Question

The restaurant in the Space Needle in Seattle rotates at the rate of one revolution per hour. (Round your answers to two decimal places.)
(b) How long does it take the restaurant to rotate through 8 radians?
(c) How far does a person sitting by the window move in 140 minutes if the radius of the restaurant is 21 meters?

Answer 1

a) 130 mins = 2 hours 10 mins or 2 and 1/6 hours... so 2 and 1/6 revolution. and 1 revolution is equal to 2*pi radians 
ANSWER: 13/6 (2 and 1/6) * 2*pi = 13.6 radians 

b) 8/13.6 = x/(13/6) so x = 0.2715 hours or 16 and 1/3 minutes 

c) if the restaurant is 21 meters, the radius is 10.5 meters, and the circumference is 2*pi*r so circumference = 65.97 meters. 

2 and 1/6 revolution is going around the circumference 2 and 1/6 times, so simply multiply 65.97 by 13/6 

ANSWER: about 143 meters