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The diameter of a circle is 16. By what number must the radius be decreased in order to decrease the area of the circle by 48 pi?

 Nov 6, 2017
 #1
avatar+99297 
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The diameter of a circle is 16. By what number must the radius be decreased in order to decrease the area of the circle by 48 pi?

 

I really am not sure what you are asking.....

 

The original area is   pi*64    if you want to decrease this by 48pi  then the new area must be 16pi units^2

 

So the radius would have to be 4 units, the diameter would be 8 units.

This is half of the orginal diameter. 

 Nov 6, 2017
 #2
avatar+98125 
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The current radius  is   diameter/ 2  = 16/ 2  =  8

 

And area  = pi * r^2

 

So....the current area is  pi (8)^2  = 64pi  units^2

 

Reducing by 48 pi units^2  means that he new area is  [ 64 pi - 48 pi ]  =  16 pi units^2

 

So......16 pi  = pi (r^2)       .....divide both sides by  pi ......  

 

16  = r^2  ⇒    4  = r

 

So....the current radius must be halved to reduce the area by 48 pi units^2

 

 

cool cool cool

 Nov 6, 2017
 #3
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That is correct.

Guest Nov 6, 2017

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