Show transcribed image text The hot air balloon is the oldest successful human airlift technology. I

Show transcribed image text The hot air balloon is the oldest successful human airlift technology. Its simplistic design allows for a fundamental understanding of variational design. Consider the design of an airship with a cylindrical body and hemispherical sides as shown. The objective is to create a design driven by engineering principles and parametric modeling. Let this airship fly at certain altitude and maintain its height for a period of time. The initial design requires that the airship must be fit to carry its prescribed load. Provide the necessary information and derive the engineering function that allows us to determine the maximum payload requirements as function of the design parameters. We take r belongs to [0, 15] and a belongs to [0,75].