Notes
Problems & Solutions
\(\textbf{1)}\) Find the length of the red arc.
\(\,\,\,\)The arc length is \(\displaystyle\frac{22\pi}{9}\) units\( \approx 7.67945\) units
\(\,\,\,\,\,\,\,\,\,\text{Arc Length}=\displaystyle\frac{n^{\circ}}{180^{\circ}}\cdot \pi r\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{110^{\circ}}{180^{\circ}}\cdot \pi (4)\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{22\pi}{9}\)
\(\,\,\,\,\,\,\,\,\,\)The arc length is \(\displaystyle\frac{22\pi}{9}\) units\( \approx 7.67945\) units
![Link to Youtube Video Solving Question Number 1](https://andymath.com/wp-content/uploads/2020/08/play-video.jpg")
\(\textbf{2)}\) Find the length of the red arc.
\(\,\,\,\)The arc length is \(\displaystyle\frac{20\pi}{3}\) units\( \approx 20.944\) units
\(\,\,\,\,\,\,\,\,\,\text{Arc Length}=\displaystyle\frac{n^{\circ}}{180^{\circ}}\cdot \pi r\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{150^{\circ}}{180^{\circ}}\cdot \pi (8)\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{20\pi}{3}\)
\(\,\,\,\,\,\,\,\,\,\)The arc length is \(\displaystyle\frac{20\pi}{3}\) units\( \approx 20.944\) units
\(\textbf{3)}\) Find the length of the red arc.
\(\,\,\,\)The arc length is \(\displaystyle\frac{85\pi}{9}\) units\( \approx 29.6706\) units
\(\,\,\,\,\,\,\,\,\,\text{Arc Length}=\displaystyle\frac{n^{\circ}}{180^{\circ}}\cdot \pi r\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{170^{\circ}}{180^{\circ}}\cdot \pi (10)\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{85\pi}{9}\)
\(\,\,\,\,\,\,\,\,\,\)The arc length is \(\displaystyle\frac{85\pi}{9}\) units\( \approx 29.6706\) units
\(\textbf{4)}\) Find the length of the red arc.
\(\,\,\,\)The arc length is \(\displaystyle\frac{14\pi}{3}\) units\( \approx 14.6608\) units
\(\,\,\,\,\,\,\,\,\,\text{Arc Length}=\displaystyle\frac{n^{\circ}}{180^{\circ}}\cdot \pi r\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{280^{\circ}}{180^{\circ}}\cdot \pi (3)\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{14\pi}{3}\)
\(\,\,\,\,\,\,\,\,\,\)The arc length is \(\displaystyle\frac{14\pi}{3}\) units\( \approx 14.6608\) units
\(\textbf{5)}\) Find the length of the red arc.
\(\,\,\,\)The arc length is \(5\pi\) units\( \approx 15.708\) units
\(\,\,\,\,\,\,\,\,\,\text{Arc Length}=\displaystyle\frac{n^{\circ}}{180^{\circ}}\cdot \pi r\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{The diameter is } 10, \text{so the radius is } \frac{10}{2}=5\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\displaystyle\frac{180^{\circ}}{180^{\circ}}\cdot \pi (5)\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\pi\)
\(\,\,\,\,\,\,\,\,\,\)The arc length is \(5\pi\) units\( \approx 15.708\) units
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