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, \(r = 52\) cm and \(\theta=270^{\circ}\).

Step3: Substitute the values into the formula

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First, calculate \(3\times3.14 = 9.42\), then \(9.42\times52=489.84\), and finally \(\frac{489.84}{2}=244.92\)

Answer:

\(244.92\)