A wheel with a 18inch diameter is turning at the rate of 48

A wheel with a 18-inch diameter is turning at the rate of 48 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min?

Solution

A point on the rim travels a distance, c, equal to the circumference of the wheel of diameter, d, for each revolution of the wheel.
Then we have
(1) c = pi*d in/rev or
(2) c = 18*pi in/rev
Now multiply (2) by the turning rate of 48 rev/min to get the speed, s,
(3) s = (18*pi in/rev)*(48 rev/min) or
(4) s = 18*48*pi in/min or
(5) s = 2714 in/min