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 = wh. 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?
Make a short answer
Product: Box of cereal
Dimensions: Length = 8 inches, Width = 4 inches, Height = 2 inches
Surface Area (SA) = 2(8)(4) + 2(4)(2) + 2(8)(2) = 64 + 16 + 32 = 112 square inches
Volume (V) = 8(4)(2) = 64 cubic inches
Ratio of Surface Area to Volume = SA/V = 112/64 = 1.75
The ratio of surface area to volume for the box of cereal is 1.75. This means that for every 1 cubic inch of cereal inside the box, there is 1.75 square inches of surface area on the outside of the box. This ratio helps manufacturers optimize packaging by efficiently using materials while maximizing the amount of product that can be stored inside.