This question consists of 4 sub-questions, and the answer to each sub-question is an integer between 000 and 999. Please fill in the correct answer on the blank.

1. Inside a cylinder with a base radius of 6, there are two spherical surfaces with a radius of 6, and the distance between their centers is 13. If a plane is made to be tangent to these two spherical surfaces and intersects the cylindrical surface to form an ellipse, then the sum of the lengths of the major axis and the minor axis of this ellipse is ( ).

)
25
II. Fill-in-the-blank Questions
1. 【Analysis and Solution】Through the point of tangency between the plane and the sphere, draw the axial section of the cylinder (as shown in the figure). Clearly, the minor axis of the ellipse is the diameter of the cylinder, i.e., $2 b=12$.
$$
\begin{array}{l}
\text { Also } \cos \alpha=6: \frac{13}{2}=\frac{12}{13}, \\
\because a=\frac{6}{\cos \alpha}=\frac{13}{2}, \\
\because 2 a=13,2 a+2 b=25 .
\end{array}
$$