Problem

2014 AMC 8 Problem 20

Rectangle $ABCD$ has sides $CD=3$ and $DA=5$ . A circle with a radius of $1$ is centered at $A$ , a circle with a radius of $2$ is centered at $B$ , and a circle with a radius of $3$ is centered at $C$ . Which of the following is closest to the area of the region inside the rectangle but outside all three circles? [asy] draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); draw(Circle((0,0),1)); draw(Circle((0,3),2)); draw(Circle((5,3),3)); label("A",(0.2,0),W); label("B",(0.2,2.8),NW); label("C",(4.8,2.8),NE); label("D",(5,0),SE); label("5",(2.5,0),N); label("3",(5,1.5),E);[/asy]

$\textbf{(A) }3.5\qquad\textbf{(B) }4.0\qquad\textbf{(C) }4.5\qquad\textbf{(D) }5.0\qquad\textbf{(E) }5.5$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Category: AMC 8
Points: 2
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