Question

what is the length of an arc with a central angle of 180° and a diameter of 18 centimeters? round to the nearest tenth.

Explanation:

Step1: Find the radius

Since the diameter \(d = 18\) cm, and \(r=\frac{d}{2}\), then \(r=\frac{18}{2}=9\) cm.

Step2: Use the arc - length formula

The formula for the length of an arc is \(L=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius.
Given \(\theta = 180^{\circ}\) and \(r = 9\) cm.
Substitute into the formula: \(L=\frac{180}{360}\times2\pi\times9\).
Simplify \(\frac{180}{360}=\frac{1}{2}\), then \(L=\frac{1}{2}\times2\pi\times9\).
The \(2\)s cancel out, so \(L = 9\pi\).
Using \(\pi\approx3.14\), then \(L\approx9\times3.14 = 28.26\) cm.
Rounding to the nearest tenth, \(L\approx28.3\) cm.

Answer:

\(28.3\) centimeters