Question

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

Explanation:

Step1: Find the radius

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

Step2: Use arc - length formula

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

Step3: Calculate the arc - length

$l=\frac{123}{360}\times20\pi=\frac{123\pi}{18}\approx\frac{123\times3.14}{18}=\frac{386.22}{18}\approx21.5$ cm.

Answer:

21.5 centimeters