Question

Volume and surface area are often compared by manufacturers 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.

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 using the formula SA = 2lw + 2wh + 2lh.
The volume of a rectangular prism can be found using the formula V = lwh. Write
an expression for the ratio of surface area to volume for the figure.

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's consider packaging a stack of books in a rectangular prism shaped box.

Let's assume the length of the box is 10 inches, the width is 8 inches, and the height is 6 inches.

Surface Area = 2(10)(8) + 2(8)(6) + 2(10)(6) = 160 + 96 + 120 = 376 sq. in.

Volume = 10 x 8 x 6 = 480 cu. in.

Ratio of Surface Area to Volume = Surface Area/Volume = 376/480 ≈ 0.7833

So, the ratio of surface area to volume for packaging a stack of books in a rectangular box with dimensions 10 x 8 x 6 is approximately 0.7833.