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The above shows 2 congruent circles that are enclosed within a rectangle. Each circle passes through the center of the other circle. Each circle has an area of 10 units.

 

To the nearest whole number, what is the area of the rectangle?

 

 Jan 8, 2020
 #1
avatar+109061 
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The area of a circle  =  pi * r^2

 

So....to find the radius of each circle  we have that

 

10  = pi * r^2

 

10 / pi  = r^2

 

 

The width of the rectangle  = 3r

And  the height = 2r

 

So.....the area =   3r * 2r  =   6r^2  =  6 (10 / pi)  =  60 /pi  ≈  19.1 units^2  ≈  19  units^2 

 

EDIT TO CORRECT AN EARLIER ERROR  !!!! 

 

 

cool cool cool

 Jan 8, 2020
edited by CPhill  Jan 9, 2020
 #2
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Chris, I'm baffled.  How is the width 4 radii?  It looks like 3 to me.  ~scratching my head~   

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Guest Jan 8, 2020
 #3
avatar+109061 
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OOPS...I made a mistake.....let me fix that  !!!

 

THX for the correction!!!

 

cool cool cool

CPhill  Jan 9, 2020

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