1. The problem describes a circle centered at $(2,3)$ with radius $2$ units. 2. The general equation of a circle with center $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. Substituting the given center and radius: $$ (x - 2)^2 + (y - 3)^2 = 2^2 $$ $$ (x - 2)^2 + (y - 3)^2 = 4 $$ 4. The graph shows the upper half of the circle shaded (gray) and the lower half white. 5. To find the area of the shaded region (upper half), we calculate half the area of the full circle. 6. The area of a full circle is: $$ \pi r^2 = \pi \times 2^2 = 4\pi $$ 7. Therefore, the area of the upper half (shaded region) is: $$ \frac{1}{2} \times 4\pi = 2\pi $$ 8. The problem asks to identify the interval containing the area $A$ of the shaded region. 9. Since $A = 2\pi$, it lies in the interval: $$ 2\pi < A < 3\pi $$ 10. Hence, the correct choice is A. Final answer: $A = 2\pi$ which satisfies $2\pi < A < 3\pi$.