Enviro Design A: Cone-topped Cylinder Instructions MSeaV has hired you to design a new prototype for an environmentally friendly plastic water bottle. The water bottle is to have a volume of Y50cm3. You are to consider a cylindrical 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 6 cm and the height of the conical piece should be equivalent to its radius. Determine the dimensions and resulting surface area for a cone topped cylindrical plastic water 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}