Answer
The radius of the spool is $~~3.73~cm$
Work Step by Step
The thread is being pulled off the spool at a rate of 59.4 cm per second. We can find the length of thread that is pulled off the spool in one minute:
$(59.4~cm/s)(60~s) = 3564~cm$
We can think of this length as the arc length $S$ as the spool rotates for one minute.
Thus: $~~S = 3564~cm$
The spool makes 152 revolutions per minute. We can find the angle in radians through which the spool rotates in one minute:
$\theta = (2\pi)(152) = (304~\pi)~radians$
We can find the radius $r$ of the spool:
$S = r~\theta$
$r = \frac{S}{\theta}$
$r = \frac{3564~cm}{304~\pi}$
$r = 3.73~cm$
The radius of the spool is $~~3.73~cm$
