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.

Answer 1

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.

Answer 2

By optimizing the volume to surface area ratio, manufacturers can save on material costs, maximize storage efficiency, and reduce overall environmental impact. For example, a company may choose to design packaging with a larger volume and smaller surface area to fit more products while using less material, ultimately reducing packaging waste and transportation costs. On the other hand, if the surface area is too large in relation to the volume, it may result in excess material usage, leading to higher production costs and potential environmental consequences. Therefore, finding the right balance between volume and surface area is essential for manufacturers to produce sustainable and cost-effective packaging solutions.

Answer 3

One example of a product that might be packaged in the shape of a rectangular prism is a box of cereal. Cereal boxes are typically rectangular prisms with the product stacked inside. The dimensions of the box (length, width, and height) can vary depending on the brand and packaging design. The surface area of the cereal box can be calculated using the formula SA = 2lw + 2wh + 2lh, where l is the length, w is the width, and h is the height of the box. Manufacturers may use this formula to optimize the packaging design, maximizing the volume of cereal that can be stored inside while minimizing the amount of material needed to create the box.