The main objective of Computer Aided Geometric Design (CAGD) is the construction of a decent Bezier curve that satisfies design requirements and ensures high manufacturing efficiency. This research aims to investigate the behavior of the Bezier curve with shape parameters (α, λ, s) resulting in Generalized Bezier curves. The main goal is to yield minimum surface area from the Generalized Bezier surface of revolution to enhance manufacturing efficiency, material usage, and fabrication. To study the influence of shape parameters on curve geometric morphology, it is required to generate a miscellaneous design with a range of shape parameter values and then statistically evaluate. Also, the Taguchi method has been used to investigate the most significant contribution of each parameter that yields the minimum surface area. ANOVA results indicate that the parameters S & λ have the most significant influence on the (SA). The results clarified the non-linear behavior between shape parameters that makes the direct prediction of curve configuration intricate for variations of shape parameters, especially for S-curve shapes.