imc

A line going through the centers of the two smaller circles also goes through the diameter. The length of this line within the circle is $3+3+2+2=10.$ Because this is the length of the larger circle's diameter, the length of its radius is $5.$ The area of the large circle is $25\pi$, and the area of the two smaller circles is $9\pi +4\pi =13\pi .$ To find the area of the shaded region, subtract the area of the two smaller circles from the area of the large circle. $⟶25\pi -13\pi =\boxed{12\pi }$