Question

find the length of arc abc. use 3.14 for the value of π. round to the nearest hundredth of a cm.

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) of a circle is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Identify the values of \(\theta\) and \(r\)

From the problem, \(\theta = 240^{\circ}\) and \(r = 54\) cm.

Step3: Substitute the values into the formula

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First, calculate \(2\times3.14\times54 = 339.12\). Then, \(\frac{2}{3}\times339.12=226.08\)

Answer:

\(226.08\)