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The Five-hundred-meter Aperture Spherical radio Telescope (FAST), the largest single-dish radio telescope in the world, has implemented an innovative technology for its huge reflector, which changes the shape of the primary reflector from spherical to that of a paraboloid of 300-m aperture. Here, we explore how the current FAST sensitivity can potentially be further improved by increasing the illuminated area (i.e. the aperture of the paraboloid embedded in the spherical surface). Alternatively, the maximum zenith angle can be increased to give greater sky coverage by decreasing the illuminated aperture. Different parabolic apertures within the FAST capability are analyzed in terms of how far the spherical surface would have to move to approximate a paraboloid. The sensitivity of FAST can be improved by approximately 10 per cent if the aperture of the paraboloid is increased from 300 to 315 m. The parabolic aperture lies within the main spherical surface and does not extend beyond its edge. The maximum zenith angle can be increased to approximately 35º from |$26{_{.}^{\circ}}4$|⁠ , if we decrease the aperture of the paraboloid to 220 m. This would still give a sensitivity similar to the Arecibo 305-m radio telescope. Radial deviations between paraboloids of different apertures and the spherical surfaces of differing radii are also investigated. Maximum zenith angles corresponding to different apertures of the paraboloid are further derived. A spherical surface with a different radius can provide a reference baseline for shape-changing applied through active reflector technology to FAST-like telescopes. [ABSTRACT FROM AUTHOR]