A circle has a radius of 4 . An arc in this circle has a central angle of $$288^{\circ}$$. What is the length of the arc? Enter an exact answer in terms of $$\pi$$. 

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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>A circle has a radius of 4 . An arc in this circle has a central angle of $$288^{\circ}$$. What is the length of the arc? Enter an exact answer in terms of $$\pi$$. 

![](http://admin.getprephub.com/media/editor/ci10_20230216204237938992.png)</textarea>A circle has a radius of 4 . An arc in this circle has a central angle of <math><semantics><mrow><mn>2</mn><mn>8</mn><msup><mn>8</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex">288^{\circ}</annotation></semantics></math>288​∘​​. What is the length of the arc? Enter an exact answer in terms of <math><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math>π. 
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>A circle has a radius $$r=4$$.

An arc in this circle has a central angle $$\theta=288^{\circ}=\frac{288 \pi}{180}$$

The length of the arc $$(s)=r \theta=\frac{288 \pi}{180} \times 4=6.4 \pi$$

</textarea>A circle has a radius <math><semantics><mrow><mi>r</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">r=4</annotation></semantics></math>r=4.
An arc in this circle has a central angle <math><semantics><mrow><mi>θ</mi><mo>=</mo><mn>2</mn><mn>8</mn><msup><mn>8</mn><mrow><mo>∘</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>2</mn><mn>8</mn><mn>8</mn><mi>π</mi></mrow><mrow><mn>1</mn><mn>8</mn><mn>0</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">\theta=288^{\circ}=\frac{288 \pi}{180}</annotation></semantics></math>θ=288​∘​​=​180​​288π​​
The length of the arc <math><semantics><mrow><mo>(</mo><mi>s</mi><mo>)</mo><mo>=</mo><mi>r</mi><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mn>8</mn><mn>8</mn><mi>π</mi></mrow><mrow><mn>1</mn><mn>8</mn><mn>0</mn></mrow></mfrac><mo>×</mo><mn>4</mn><mo>=</mo><mn>6</mn><mi mathvariant="normal">.</mi><mn>4</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">(s)=r \theta=\frac{288 \pi}{180} \times 4=6.4 \pi</annotation></semantics></math>(s)=rθ=​180​​288π​​×4=6.4π
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