A circle has a radius of $$6$$ units.An arc in this circle has a central angle of $$48$$ degrees.

What is the length of the arc?Enter an exact answer in terms of $$\pi$$ and enter your answer as a decimal.

![](http://admin.getprephub.com/media/editor/ci13_20230216204501866963.png)

<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>A circle has a radius of $$6$$ units.An arc in this circle has a central angle of $$48$$ degrees.

What is the length of the arc?Enter an exact answer in terms of $$\pi$$ and enter your answer as a decimal.

![](http://admin.getprephub.com/media/editor/ci13_20230216204501866963.png)</textarea>A circle has a radius of <math><semantics><mrow><mn>6</mn></mrow><annotation encoding="application/x-tex">6</annotation></semantics></math>6 units.An arc in this circle has a central angle of <math><semantics><mrow><mn>4</mn><mn>8</mn></mrow><annotation encoding="application/x-tex">48</annotation></semantics></math>48 degrees.
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 and enter your answer as a decimal.
<img src="http://admin.getprephub.com/media/editor/ci13_20230216204501866963.png" alt="">
</div>

<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Given that,

Radius $$(r)=6$$ and central angle $$(\theta) 48^{\circ}=\frac{48 \pi}{180}$$

The length of the $${arc}(s)=\frac{48 \pi}{180} \times 6=1.6 \pi$$
</textarea>Given that,
Radius <math><semantics><mrow><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">(r)=6</annotation></semantics></math>(r)=6 and central angle <math><semantics><mrow><mo>(</mo><mi>θ</mi><mo>)</mo><mn>4</mn><msup><mn>8</mn><mrow><mo>∘</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>4</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) 48^{\circ}=\frac{48 \pi}{180}</annotation></semantics></math>(θ)48​∘​​=​180​​48π​​
The length of the <math><semantics><mrow><mrow><mi>a</mi><mi>r</mi><mi>c</mi></mrow><mo>(</mo><mi>s</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mn>8</mn><mi>π</mi></mrow><mrow><mn>1</mn><mn>8</mn><mn>0</mn></mrow></mfrac><mo>×</mo><mn>6</mn><mo>=</mo><mn>1</mn><mi mathvariant="normal">.</mi><mn>6</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">{arc}(s)=\frac{48 \pi}{180} \times 6=1.6 \pi</annotation></semantics></math>arc(s)=​180​​48π​​×6=1.6π
</div>