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# Geometry

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A sector of a circle has a central angle of 100. If the area of the sector is 250\pi, what is the radius of the circle?

May 27, 2022

#1
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What is the radius of the circle?

Hello Guest!

$$A=\frac{\pi r^2}{360°}\cdot\alpha\\ r=\sqrt{\frac{360°\cdot A}{\pi\cdot \alpha}}\\ r=\sqrt{\frac{360°}{\pi\cdot 100°}\cdot \frac{250}{\pi}}=\dfrac{1}{\pi}\cdot \sqrt{36\cdot 25}\\ \color{blue}r=\dfrac{30}{\pi}=9.549$$

!

May 27, 2022