Envlro Design A: Cone-topped Cylinder lnsb'uctione MSeev has hired you to design a new prototype for an environmenlally friendly plastic weler bottle. The water bottle is to have a volume of im You are to consider a ovlindncal model that is topped by a cone. The design would have a snip off top so no cap would be needed. For ergonomic purposes: the radius should be at least 3 cm and at most ES cm and the height of the conical piece should be equivalentto its radius Determine the dimer'isions and resulting surface area for a bone topped cylindrical plastic 1lvater bottle that minimizes the amount of plastic used. Provide a solution to this problem with evidence of a plan to solve an optimization problem that Includes an algebraic solution using calculus techniques (differentiation. solving for extreme values, testing interval endpoints. etc)