Four cubes with edge lengths $1$, $2$, $3$, and $4$ are stacked as shown. What is the length of the portion of $\overline{XY}$ contained in the cube with edge length $3$?

$\textbf{(A)}\ \dfrac{3\sqrt{33}}5\qquad\textbf{(B)}\ 2\sqrt3\qquad\textbf{(C)}\ \dfrac{2\sqrt{33}}3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 3\sqrt2$
By Pythagorean Theorem in three dimensions, the distance $XY$ is $\sqrt{4^2+4^2+10^2}=2\sqrt{33}$.
Let the length of the segment $XY$ that is inside the cube with side length $3$ be $x$. By similar triangles, $\dfrac{x}{3}=\dfrac{2\sqrt{33}}{10}$, giving $x=\boxed{\textbf{(A) }\dfrac{3\sqrt{33}}{5}} skr-$.