Question

consider circle t with radius 24 in. and ( \theta=\frac{21}{8} ) radians. what is the length of minor arc sv? ( 63 pi ) in. ( 28 pi ) in. ( 40 pi ) in. ( 20 pi ) in.

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

Given \(r = 24\) in and \(\theta=\frac{7\pi}{8}\) radians.

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Step3: Simplify the expression

First, simplify \(24\times\frac{7\pi}{8}\). Since \(\frac{24}{8}=3\), then \(24\times\frac{7\pi}{8}=3\times7\pi = 21\pi\) (This is wrong, let's correct it).

Wait, no, if \(\theta=\frac{21}{8}\) radians (maybe a mis - read before). Given \(r = 24\) in and \(\theta=\frac{21}{8}\) radians.

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Since \(\frac{24}{8}=3\), then \(s = 3\times21\pi=63\pi\)

Answer:

\(63\pi\) in.