A thread is being pulled off a spool at the rate of $71.3 \mathrm{~cm}$ per sec. Find the radius of the spool if it makes 154 revolutions per min.
$r \approx \square \mathrm{cm}$
(Round to two decimal places as needed.)
Answer
Final Answer: The radius of the spool is approximately \(\boxed{4.42 \mathrm{~cm}}\).
Step 1 ：Convert the revolutions per minute to revolutions per second: \(\frac{154}{60} = 2.566666666666667\) revolutions per second.
Step 2 ：Set up the equation for the circumference of the circle, which the thread is tracing: \(2\pi r = 71.3\) cm per second.
Step 3 ：Solve the equation for r, the radius of the spool: \(r = \frac{71.3}{2\pi \times 2.566666666666667} = 4.4212003022540785\) cm.
Step 4 ：Round the radius to two decimal places: \(r \approx 4.42\) cm.
Step 5 ：Final Answer: The radius of the spool is approximately \(\boxed{4.42 \mathrm{~cm}}\).
