Question

find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. express the arc length in terms of π. then round your answer to two decimal places. radius, r = 19 inches; central angle, θ = 180°. s = inches (simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.) s = inches (round to two decimal places as needed.)

Explanation:

Step1: Recall 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. First, convert the angle from degrees to radians. We know that \(180^{\circ}=\pi\) radians.

Step2: Calculate arc - length in terms of \(\pi\)

Given \(r = 19\) inches and \(\theta=\pi\) radians, substitute into the formula \(s=r\theta\). So \(s = 19\times\pi=19\pi\) inches.

Step3: Calculate the approximate value

To find the approximate value, substitute \(\pi\approx3.14159\) into \(s = 19\pi\). Then \(s\approx19\times3.14159 = 59.69021\approx59.69\) inches.

Answer:

\(s = 19\pi\) inches
\(s\approx59.69\) inches