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Circle $A$ has its center at $A(4, 4)$ and has a radius of 4 units. Circle $B$ has its center at $B(12, 4)$ and has a radius of 4 units. What is the area of the gray region bound by the circles and the $x$-axis? Express your answer in terms of $\pi$.

 

 

 Dec 28, 2020
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We can construct  a rectangle with  width  AB  = 4 + 4  = 8   and a height of   4

 

The area of  this rectangle  =  8 * 4   = 32

 

Note that the gray area  =  area  of  the rectangle  less the  area of  two quarter-circles  with a radius of  4 =

 

32    -  2   [pi(4^2) / 4]  =

 

32  -       (16pi ) / 2  =

 

[32  -  8pi]  units^2

 

 

cool cool cool

 Dec 28, 2020

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