1. (10 points) As shown in the figure, a square pond with a side length of 12 meters is surrounded by grass. There are wooden stakes at points $A$, $B$, $C$, and $D$ on the pond's edge, and $A B=B C=C D=3$ meters. Now, a 4-meter-long rope is used to tie a sheep to one of these wooden stakes. To maximize the area where the sheep can graze on the grass, the rope should be tied to the stake at $\qquad$.
1. (10 points) As shown in the figure, a square pond with a side length of 12 meters is surrounded by grass. There are wooden stakes at points $A$, $B$, $C$, and $D$ on the pond's edge, and $AB = BC = CD = 3$ meters. Now, a 4-meter-long rope is used to tie a sheep to one of these stakes. To maximize the area where the sheep can graze on the grass, the rope should be tied to the stake at $\qquad$ $B$.

【Analysis】Calculate the area of the sectors formed with $A$, $B$, $C$, and $D$ as the centers, and then compare them to choose the correct answer.

【Solution】Solution: (1) $S_{A}=\frac{1}{2} \pi \times 4^{2}+\frac{1}{4} \pi \times(4-3)^{2}=8.25 \pi$ (square meters);
(2) $S_{B}=\frac{3}{4} \pi \times 4^{2}=12 \pi$ (square meters);
(3) $S_{C}=\frac{1}{2} \pi \times 4^{2}+\frac{1}{4} \pi \times(4-3)^{2}=8.25 \pi$ (square meters);
(4) $S_{D}=\frac{1}{2} \pi \times 4^{2}=8 \pi$ (square meters),
$$
\pi<8.25 \pi<12 \pi,
$$

Therefore, to maximize the area where the sheep can graze on the grass, the rope should be tied to the stake at $B$.
The answer is: $B$.