jmc

The area of the visible shaded region is equal to the area of the grid minus the area of the five circles. The diameter of the four smaller circles is equal to a side of a small square, or 2 cm, so the radius of each of the smaller circles is 1 cm. The area of all four circles is then $4\cdot \pi \cdot 1^2=4\pi$. The diameter of the large circle is equal to the length of three sides of a small square, or 6 cm, so the radius of the large circle is 3 cm. The area of the large circle is then $\pi \cdot 3^2=9\pi$. Each side of the grid measures $5\cdot 2=10$ cm, so the area of the grid is $10\cdot 10=100$. The area of the visible shaded region is thus $100-4\pi -9\pi =100-13\pi$ square cm. So $A=100$, $B=13$, and $A+B=100+13=\boxed{113}$.