An object travels along a circular path so that it completes one revolution in 8 seconds. if the linear velocity of the object is 90π inches per minute, what is the diameter, in inches, of the circular path? a) 5.625 b) 6 c) 11.25 d) 12

For a circle of diameter d, one complete revolution has length
  C = π*d
The linear speed is the ratio of length to time. The problem statement tells us
  C/(8 seconds) = (90π in)/(60 seconds)
Substituting for C, we get
  (π*d)/(8 s) = (90π in)/(60 s)

Multiplying this by (8 s)/π gives
  d = (8*90/60) in
  d = 12 in

The appropriate choice is ...
  d) 12