Have you ever wondered why cereal comes in a box, and soup in a can? This is a question that can be somewhat answered by finding the volume and surface area of products and evaluating their efficiency.
If we are talking about food packaging the Volume is the amount of food the container can hold. Whereas Surface Area is the amount of material that it takes to make the package, and just to recap the Perimeter is the distance around the outside of an object. Essentially, the surface area is the sum of all the areas of all the individual sides.
| Shape Name | Rectangle/Square | Circle | Cylinder |
|---|---|---|---|
| Shape | |||
| Formula | Perimeter $p=2l+2w$ | Circumference $c = 2\pi r$ | Surface Area $S= 2\pi r^2+2\pi rh$ |
| Shape Name | Box | Sphere | Cone |
|---|---|---|---|
| Shape | |||
| Formula | Surface Area $S = 2lw + 2lh + 2wh$ | Surface Area $S = 4\pi r^2$ | Surface Area $S = \pi r^2 + \pi r l$ |
The efficiency for packages comes in when you start to compare the volume to the surface area. Efficiency basically means how can we maximize volume while minimizing price to create the packaging. For maximum efficiency we need to make the volume as large as possible while making the surface area as small as possible. Typically the higher the volume to surface area ratio the more efficient the package. In order to actually find measurements for this you'd need to do rather complex mathematics. But, for the sake of this lesson we will just use trial and error.
A company has hired you to figure out what would be the most efficient packaging for their new protein pancake mix. They want to determine if a box or a canister would be a more efficient packaging. Pictures of both with dimensions are outlined below. Which package is more efficient and why?
To determine the efficiency we need to find the volume and the surface area of each shape:
The cylinder has the smaller surface area while holding the same volume, making it the more efficient packaging choice.