You want to make cylindrical containers to hold 1 liter using the least amount of construction material. The side is made from a rectangular piece of material, and this can be done with no material wasted. However, the top and bottom are cut from squares of side 2r, so that 2(2r)2 = 8r2 of material is needed (rather than 2πr2, which is the total area of the top and bottom). Find the dimensions of the container using the least amount of material, and also ﬁnd the ratio of height to radius for this container

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