In a circle, a 270° sector has area 300s in? What is the radius of the circle?
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04-04-2022
Mathematics

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In a circle, a 270° sector has area 300s in? What is the radius of the circle?
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Sagot :

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jdoe0001 jdoe0001 · Answer 1 · 2022-04-04T16:44:51-04:00

jdoe0001 jdoe0001

04-04-2022

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=300\pi \\ \theta =270 \end{cases}\implies 300\pi =\cfrac{(270)\pi r^2}{360}\implies 300\pi =\cfrac{3\pi r^2}{4} \\\\\\ 1200\pi =3\pi r^2\implies \cfrac{1200\pi }{3\pi }=r^2\implies 400=r^2\implies \sqrt{400}=r\implies 20=r[/tex]

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