b.Choose an appropriate length, width, and height for your package so that it can fit the product that you’re shipping. Using these dimensions, what is the ratio of surface area to volume?

Question

~~The volume and surface area are often compared by companies in order to maximize how much of something can go inside of a package (volume) while keeping how much material is required to create the package (surface area) low.
a.Pick a product that might be packaged in the shape of a rectangular prism. A rectangular prism has three dimensions: length, width, and height. The surface area of a rectangular prism can be found with the formula SA = 2lw + 2wh + 2lh. The volume of a rectangular prism can be found with the formula V = lwh. Write an expression for the ratio of surface area to volume for the figure.
b.Choose an appropriate length, width, and height for your package so that it can fit the product that you’re shipping. Using these dimensions, what is the ratio of surface area to volume?

Answer 1

SA/Vol=2(LW+LH+HW)/LWH=2(1/H + 1/W + 1/L).

If all three dimensions are the same (cube) then the above expression comes to 6/X where X is the side length. This is the same as 6X^2/X^3, which is the area of 6 square faces divided by the volume. 

To answer the question we need to know the dimensions of what you're packing. The object doesn't have to be a regular shape, because all you need is to work out the the widest, longest and deepest (tallest) parts of the object. If you were doing this practically you could take two books (for example) and measure how far apart they would need to be in parallel to accommodate the length, width and height separately. Remember a cube gives the maximum amount of volume, so if you were packing many small objects into one box, they would probably fit best into a cube.

So there's no answer to your question until you have something to pack!