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 circular path 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 the linear speed is ...

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