Question

in a circle with a radius of 2.8 cm, an arc is intercepted by a central angle of \\( \frac{\pi}{5} \\) radians. what is the arc length? use 3.14 for \\( \pi \\) and round your final answer to the nearest hundredth. enter your answer as a decimal in the box. cm

Explanation:

Step1: Recall the arc - length formula

The formula for the arc length \(s\) of a circle is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 2.8\space cm\) and \(\theta=\frac{\pi}{5}\). Substitute into \(s = r\theta\), we get \(s=2.8\times\frac{\pi}{5}\). Since \(\pi = 3.14\), then \(s = 2.8\times\frac{3.14}{5}\).
First, calculate \(2.8\times3.14=8.792\). Then \(s=\frac{8.792}{5}\).

Step3: Perform the division

\(s = 1.7584\). Rounding to the nearest hundredth (two decimal places), we look at the third decimal digit. The third decimal digit is \(8\), and using the rounding rule (if the third digit is \(5\) or greater, we round up the second digit). So \(s\approx1.76\).

Answer:

\(1.76\)