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In the diagram, the three concentric circles have radii of 4, 6, and 7. Three regions are labeled X, Y, or Z below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form.

Guest Feb 23, 2017
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 #1
avatar+4152 
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So all you are doing is the area of circle Z minus the area of circle X.

The area of a circle is pi times the radius squared.

 

Circle Z has a radius of 7.

Circle X has a radius of 4.

So

the area of circle Z = (pi)(72) = 49pi , and

the area of circle X = (pi)(42) = 16pi .

 

49pi - 16pi = 33pi

hectictar  Feb 23, 2017
 #2
avatar+75287 
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Area of Region X  =  16pi

 

Area of Region Y  = 20pi

 

Area of Region Z   =  13pi

 

Difference of greatest region and smallest region  =  7pi

 

 

cool cool cool

CPhill  Mar 1, 2017

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