2018 Cayley Problem 23

A container in the shape of a triangular prism stands on one of its triangular faces. Three spheres of radius 1 are placed inside the container, each touching the triangular bottom. Each sphere touches two of the rectangular faces of the container and each sphere touches the other two spheres. A fourth sphere of radius 1 is placed on top of the three spheres, touching each of the three spheres and the top of the prism. The volume of the prism is closest to

\textbf{(A)}\ 48.00\quad \textbf{(B)}\ 47.75\quad \textbf{(C)}\ 47.50\quad \textbf{(D)}\ 47.25\quad \textbf{(E)}\ 47.00

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.