2. In the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$, the lengths of edges $A B$ and $A D$ are both 2, and the length of the body diagonal $A C_{1}$ is 3. Then the volume of the rectangular prism is $\qquad$ .
$$
A C_{1}=\sqrt{A B^{2}+A D^{2}+A A_{1}^{2}}=3 \Rightarrow A A_{1}=1 \text{, }
$$

So $V_{A B C D-A_{1} B_{1} C_{1} D_{1}}=2 \times 2 \times 1=4$.