+911 A circle with radius 4 is translated 2 units. What is the area of the region swept out by the circle?
+130042 
Translate the top circle with the equation x^2 + (y-2)^2 = 16 to the bottom circle
with the equation x^2 + y^2 = 16
Let Area A be the area of rhombus ACBD = 4^2 * sin (151.04°) ≈ 7.75
Let Area A + Area B = the area of the portion of the bottom circle bounded by minor arc CED =
pi * 4^2 * (151.04 / 360) ≈ 21.09
Area B = Area A + Area B - Area A 21.09 - 7.75 ≈ 13.35
Let Area B + Area C = the area of the portion of the top circle bounded by major arc CFD =
pi * 4^2 * ( 360 -151.04) / 360 ≈ 29.18
The area swept out by the translation of the top circle to the bottom circle =
Area B + Area C - Area B = Area C = 29.18 - 13.35 ≈ 15.84
