Question

in circle p, diameter qs measures 20 centimeters. what is the approximate length of arc qir? round to the nearest tenth of a centimeter. 19.9 centimeters 43.0 centimeters 21.5 centimeters 9.8 centimeters

Explanation:

Step1: Find the radius

Given diameter \(d = 20\) cm, radius \(r=\frac{d}{2}=\frac{20}{2}=10\) cm.

Step2: Find the central angle of arc \(QR\)

Since \(QS\) is a diameter, the central angle of arc \(QR\), \(\theta=180^{\circ}- 123^{\circ}=57^{\circ}\)

Step3: Use the arc - length formula

The arc - length formula is \(L=\frac{\theta}{360^{\circ}}\times2\pi r\). Substitute \(\theta = 57^{\circ}\) and \(r = 10\) cm.

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Answer:

\(9.9\) centimeters