Understanding the effects of interactions on the ground-state of a paired degenerate Fermi gas throughout the BEC-BCS crossover has been a long standing physical quest for which countless papers have been written. The crossover describes the smooth transition of the physics of a BEC of tightly bound dimers to that of a paired BCS superfluid. A Feshbach resonance is used to tune the interactions necessary to study the crossover. Right around resonance the interactions are expected to be parameterized by a single universal parameter beta [1--3]. This thesis describes a measurement of the axial size of paired, 6Li clouds in the BEC-BCS crossover and provides a comparison with theory. In the BEC regime, absolute measurements of the molecular scattering length are compared with the atomic scattering length and the ratio is compared with theory. Finally, a measurement of beta is made and compared with theory.