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 real-world 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 geometry-speak. 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 three-dimensional 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.
Write down these measurements for each box in centimeters. Are the dimensions fairly similar between the different boxes, or is there a lot of variation? The units will be in cm2, or centimeters squared.
How much do the surface areas vary for the different boxes? The units will be in cm3, or centimeters cubed How much do the calculated volumes vary for the different boxes? The volume of juice in the box is usually found on the front of the juice box near the bottom.
Use the volume listed in milliliters mL because 1 mL equals 1 cm3. How close is your calculated volume to the actual volume of juice in each box?
You can do this by dividing its calculated surface area by the volume of juice it holds again in milliliters. If the answer of the calculation is close to 1, the surface area and volume are almost equal. The higher the number, the more packaging is used per volume of juice; the lower the number, the less packaging is used per volume of juice.
Which box uses the least amount of packaging for the volume of juice it holds? Which box uses the most? Which one has a juice volume closest to its calculated volume and has the smallest surface-area-to-volume ratio?
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? 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 single-use cereal boxes that are only one portion size or large, multi-portion size boxes? Observations and results Was 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 surface-area-to-volume 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.
Give our editors the heads up. When Dr. Tetra Pak cartons use multiple layers of materials to ensure nothing gets in or out of the package. The cartons are made mostly of paperboard, with thin layers of plastic and aluminum working together to keep light, oxygen, and bacteria out, meaning no contamination and no preservatives needed.
By protecting the integrity of the product, the carton preserves both the taste of the food and all the essential nutrients stored inside. In fact, Tetra Pak cartons have a better package-to-product ratio than an egg. By using just the right amount of material, Tetra Pak can ensure maximum product protection while using minimal resources.
Protecting our environment, our food sources, and our natural resources is an essential part of preserving our shared future.
Remember these? What was in your lunchbox growing up? Whatever you got carrots or traded it for chips , chances are there was a juice box somewhere in the mix. From school to soccer, they were virtually everywhere—and the stuff inside always tasted great. Even today, some of us are rediscovering our love for the humble juice box.
Turns out juice boxes are even cooler than we remember. In the U. And since the introduction of the juice box into the U. But how did juice get so popular in the first place? In the nineteenth century , French scientist Louis Pasteur figured out that by heating liquids like beer, wine, and milk before packaging them, they could go longer without spoiling. And not long after that, a dentist named Dr. Thomas Bramwell Welch sound familiar?
From the bottle to the box. Before the mid-twentieth century, most drinks came in reusable glass bottles. Just picture the friendly neighborhood milkman. But in the s , Dr. Ruben Rausing began looking for a more efficient and hygienic way to package milk. He ultimately created a continuous filling system that completely filled milk cartons, leaving no room for any air that might spoil it. Want to see how it works? Click here to learn more about the innovative continuous filling process.
His unique tetrahedron-shaped paperboard milk cartons were a huge hit in Europe, where they first started appearing on shelves. Rausing then set his sights on developing a new variation of his carton, one that could be shipped and stored more easily while still keeping the contents safe. In the Tetra Brik package debuted in Dr. Its advantages were obvious: not only could it be completely filled to capacity, it was also a real space saver. The Tetra Brik carton changed the industry forever.
With their perfectly rectangular build, Tetra Brik cartons could be easily and efficiently bundled and packaged together and shipped in huge quantities. This was a real game-changer. After all, imagine stacking hundreds of 2-liter bottles on top of one another: their cylindrical shapes leave awkward gaps in between each unit.
The Tetra Brik package proved to be the perfect solution to that problem. But Dr. The Tetra Brik carton was only beginning to revolutionize the dairy industry. Just six years after the introduction of the Tetra Brik package, Dr.
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