# Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 132: 49

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 $~~3.73~cm$

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