4. Given that $A$ and $B$ are two points on a sphere with radius 5, and $AB=8$. Planes $O_{1}AB$ and plane $O_{2}AB$, which are perpendicular to each other, intersect the sphere in circles $\odot O_{1}$ and $\odot O_{2}$. Let the areas of $\odot O_{1}$ and $\odot O_{2}$ be $S_{1}$ and $S_{2}$, respectively. Then $S_{1}+S_{2}=$ $\qquad$
4. $41 \pi$.

Take the midpoint $M$ of $A B$. The radii of the two sections $\odot O_{1}$ and $\odot O_{2}$ are $r_{1}$ and $r_{2}$, respectively. Then
$$
\begin{array}{l}
S_{1}+S_{2}=\pi r_{1}^{2}+\pi r_{2}^{2} \\
=\pi\left(A M^{2}+O_{1} M^{2}+A M^{2}+O_{2} M^{2}\right) \\
=\pi\left(2 A M^{2}+O M^{2}\right) \\
=\pi\left(2 A M^{2}+O A^{2}-A M^{2}\right) \\
=\pi\left(A M^{2}+O A^{2}\right)=41 \pi .
\end{array}
$$