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The shaded sector of the circle below has an area of 4 pi what is the radius of the circle

 Nov 14, 2021
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Hi, So we know that there are 360 degrees in a cirle. 40 degrees of the circle has an area of 4pi. We know that 40/360=1/9th of the total circle so we multiply so 1/9 of the are of the circle equals 40pi

 1/9(area of the circle)=4pi

 do some algebra and get that the full circle's area is 36pi units^2.

 The equation for the are of a circle is pir^2

pir^2=36pi

divide both sides by pi

r^2=36

so this could be -6 or 6 but by convention we know that that a radius can be nagative so my answer is 6

 Nov 14, 2021

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