Juice Box Geometry
IntroductionJuice boxes sure are convenient—just poke a straw in and sip away! But have you ever noticed that some juice boxes don't seem to have as much juice as others, even when they have a lot of packaging? You might be amazed how much thought goes into designing a juice box. Each manufacturer has carefully calculated how big each side of the box needs to be to hold a certain amount of juice inside and how altering the box's dimensions affects its overall appearance and packaging. Investigating the geometry of juice boxes can reveal how some have more efficient packaging than others. And how appearances can be deceptive!
This activity is not appropriate for use as a science fair project. Good science fair projects have a stronger focus on controlling variables, taking accurate measurements, and analyzing data. To find a science fair project that is just right for you, browse our library of over 1,200 Science Fair Project Ideas or use the Topic Selection Wizard to get a personalized project recommendation.
BackgroundGeometry uses math to describe and investigate different points, lines and shapes. In geometry, the relationships among different parts of a shape can be described with mathematical formulas. Formulas can be used to describe the relationship among the three dimensions of realworld objects: length, width and height. And that information can help us learn about objects around us. A rectangular box, such as a juice box or cereal box, is called a rectangular prism in geometryspeak. If you measure the height, length and width of a rectangular prism, you can use that information in a formula to calculate the volume and surface area of that object. The volume is the amount of space an object fills in threedimensional space (which tells approximately how much a container, like a juice box, can hold), and the surface area is the total amount of area on the outer surface of the object (which tells approximately how much material was used to create the shape). Materials
Preparation
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Extra: Packaging comes in all shapes and forms. Try to use the principles of geometry to make geometric models to compare the efficiency of other shapes of packaging. For example, how do cylindrical ice cream tubs compare with rectangular ice cream tubs?
Extra: Cereal containers mostly come in rectangular shapes but can vary greatly in size. You can use different cereal boxes to investigate how geometry can help reduce waste in packaging material. Is there less wasted packaging in a large box or a small box of cereal? Is it better to buy singleuse cereal boxes that are only one portion size or large, multiportion size boxes?
Observations and ResultsWas the actual volume of juice in some juice boxes much closer to the calculated volume than when compared with other boxes? Did some boxes have a much smaller surfaceareatovolume ratio than others? As you probably saw from this activity, different juice boxes that hold the same amount of juice can have very different dimensions. This can change their surface areas and the total volumes that they can hold. The actual volume of juice held by many juice boxes takes up over 95 percent of the total calculated volume of the box, although some boxes may hold juice that takes up less of the total calculated volume than this. The surfaceareatojuicevolume ratio is usually a little over 1, often around 1.2 to 1.3. This means that there is a little more packaging used per volume of juice. The higher the ratio, the more packaging is used per volume of juice.
More to Explore"Rectangular Prism Calculator” from Calculator Soup“Cool Math 4 Kids” from Coolmath.com “Juice Box Geometry” from Science Buddies CreditsTeisha Rowland, PhD, Science Buddies
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Key Concepts
Mathematics, geometry, psychology

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