in circle p, diameter qs measures 20 centimeters. what is the approximate length of arc qr? round to the…

Explanation:

Step1: Find the radius.

The diameter $d = 20$ cm, so the radius $r=\frac{d}{2}=\frac{20}{2}=10$ cm.

Step2: Use the arc - length formula.

The formula for the length of an arc $s$ of a circle with radius $r$ and central angle $\theta$ (in degrees) is $s=\frac{\theta}{360}\times2\pi r$. Here $\theta = 123^{\circ}$ and $r = 10$ cm. So $s=\frac{123}{360}\times2\pi\times10$.

Step3: Calculate the arc - length.

First, simplify the expression: $s=\frac{123\times20\pi}{360}=\frac{123\pi}{18}$. Then, substitute $\pi\approx3.14$: $s=\frac{123\times3.14}{18}=\frac{383.22}{18}\approx21.3$. Rounding to the nearest tenth gives $s\approx21.5$ cm.

Answer:

21.5 centimeters