Question

find the length of the arc of a circle of radius 20 inches subtended by a central angle of \frac{7}{4}\pi radians. answer exactly in terms of pi. inches question help: video written example message instructor submit question

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) 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 \(r = 20\) inches and \(\theta=\frac{7}{4}\pi\) radians. Then \(s=20\times\frac{7}{4}\pi\).

Step3: Simplify the expression

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Answer:

\(35\pi\) inches