2024 Gauss 8 Problem 25

A figure is constructed using fourteen 1 \times 1 \times 1 cubes. Nine of the 1 \times 1 \times 1 cubes are used to make the bottom layer and five additional 1 \times 1 \times 1 cubes are positioned on top of the bottom layer. The figure is shown from two different perspectives. An ant begins at P and walks a distance d on the surface of the figure to arrive at Q. The smallest possible value of d is closest to

\textbf{(A)}\ 6.43\quad \textbf{(B)}\ 6.40\quad \textbf{(C)}\ 6.71\quad \textbf{(D)}\ 6.66\quad \textbf{(E)}\ 6.48

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.