2013 UNCO Math Contest II Problems/Problem 1

Problem

[asy] filldraw((-4,-3)--(-4,3)--(4,3)--(4,-3)--cycle,grey); filldraw(circle((-4,0),3),white); filldraw(circle((4,0),3),white); draw((-7,3)--(7,3),black); draw((-7,-3)--(7,-3),black); [/asy]

In the diagram, the two circles are tangent to the two parallel lines. The distance between the centers of the circles is $8$, and both circles have radius $3$. What is the area of the shaded region between the circles?


Solution

$48-9\pi$

See Also

2013 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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All UNCO Math Contest Problems and Solutions
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