1. In a rectangular frame made of metal wire with dimensions $3 \times 4 \times 7$, a ball is placed. The maximum radius of the ball is . $\qquad$
1. $\frac{5}{2}$.

If we observe the ball placed along the length of the rectangular prism, it is clear that its diameter cannot exceed the diameter of the circumcircle of the $3 \times 4$ rectangle, which is $\sqrt{3^{2}+4^{2}}=5$. Therefore, the maximum radius of the ball is $\frac{5}{2}$.