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 $\pi$.

Guest Dec 28, 2020

#1**+1 **

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

CPhill Dec 28, 2020