2015 UNCO Math Contest II Problems/Problem 2


[asy] filldraw(circle((0,0),3),white); filldraw(arc((-1,0),2,0,180)--cycle,grey); filldraw(arc((-2,0),1,0,180)--cycle,white); filldraw(arc((1,0),2,180,360)--cycle,grey); filldraw(arc((2,0),1,180,360)--cycle,white); [/asy]

Find the area of the shaded region. The outer circle has radius $3$. The shaded region is outlined by half circles whose radii are $1$ and $2$ and whose centers lie on the dashed diameter of the big circle.



See also

2015 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions