2024 Cayley Problem 5

In the diagram, the two identical bases of the prism are shaped like a star. The area of each star-shaped base is 400 cm^2. The depth of the prism (that is, the distance between the star-shaped bases) is 8 cm. The volume of the prism is

\textbf{(A)}\ 720 \text{ cm}^3\quad \textbf{(B)}\ 1520 \text{ cm}^3\quad \textbf{(C)}\ 3200 \text{ cm}^3\quad \textbf{(D)}\ 3600 \text{ cm}^3\quad \textbf{(E)}\ 28\,800 \text{ cm}^3

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 Cayley contests here.