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A sector of a circle is shown below.  The sector has an area of $60 \pi.$  What is the radius of the circle?

 

 Sep 9, 2024
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The radius of a circle can be found with the area of the circle.  The area of a sector is equal to n/360 * a where n is the angle of the sector and a is the area of the circle.

 

Using this formula,

 

60pi = 83/360 * a

 

a = 360/83 * 60pi

 

a ~ 260.24pi

 

The formula for the area of a circle is A = r^2 pi.

 

260.24pi = r^2 pi

 

260.24 = r^2

 

r ~ 16.13

 

So the radius of the circle is about 16.13.

 Sep 9, 2024

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