5. Find the arc-length of a circle with the given radius $r$ and central angle $\theta$. Give the answer in the given unit of measure.
\[
r=41 \mathrm{~km} ; \theta=14 \mathrm{rad}
\]
Answer
Final Answer: The arc-length of the circle is \(\boxed{574}\) km.
Step 1 ：The length of an arc in a circle is given by the formula \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians. In this case, the given angle is already in radians, so we don't need to convert it.
Step 2 ：Given that the radius \(r = 41\) km and the central angle \(\theta = 14\) radians, we can directly substitute the values into the formula to find the arc length.
Step 3 ：Substitute the values into the formula to find the arc length. \(s = r\theta = 41 \times 14 = 574\) km.
Step 4 ：The question asks for the length in the given unit of measure, which is kilometers. Therefore, the arc length is \(s = 574\) km.
Step 5 ：Final Answer: The arc-length of the circle is \(\boxed{574}\) km.
