These are the combined second and third stages of a full-scale model of the U.S. Navy's Standard Missile-3 (SM-3), deployed on Aegis cruisers beginning in 2004. Built by Raytheon, it is a three-stage antiballistic missile that carries a Lightweight Exoatmospheric Projectile Kinetic Warhead (LEAP KW) in its nose. After radars detect an enemy missile, the SM-3 is launched. The LEAP KW separates from the third stage and uses its seeker and Divert and Attitude Control System to home in on the missile and destroy it by physical impact (a concept known as "hit-to-kill"). This model was built and donated by Raytheon in 2005.
This object is on display in Rockets & Missiles at the Steven F. Udvar-Hazy Center in Chantilly, VA.