A packaging consultant is designing a new package for a liquid product. She can use a square based prism or a cylinder. Because of material cost restrictions,her design must have a surface area that is not more than 500 cm squared. If she wants to maximize the capacity of the package, find the dimensions of the best container of each type, to the nearest tenth of a centimeter, and thus the best overall container for the product.

Question

A packaging consultant is designing a new package for a liquid product. She can use a square based prism or a cylinder. Because of material cost restrictions,her design must have a surface area that is not more than 500 cm squared. If she wants to maximize the capacity of the package, find the dimensions of the best container of each type, to the nearest tenth of a centimeter, and thus the best overall container for  the product.