3. Given $x^{2}+y^{2}=25$. Then the maximum value of the function
$$
z=\sqrt{8 y-6 x+50}+\sqrt{8 y+6 x+50}
$$

is ( ).
(A) $5 \sqrt{10}$
(B) $6 \sqrt{10}$
(C) $7 \sqrt{10}$
(D) $8 \sqrt{10}$
3. B.

Since $x^{2}+y^{2}=25$, we have
$$
\begin{array}{l}
z=\sqrt{8 y-6 x+50}+\sqrt{8 y+6 x+50} \\
=\sqrt{(x-3)^{2}+(y+4)^{2}}+\sqrt{(x+3)^{2}+(y+4)^{2}}
\end{array}
$$

The geometric meaning is the sum of the distances from a point on the circle $x^{2}+y^{2}=25$ to points $A(3,-4)$ and $B(-3,-4)$. The maximum value is the sum of the distances from the point $(0,5)$ to $A$ and $B$, which is $6 \sqrt{10}$.