# Ask an Expert: Cereal Box Volume and Surface Area Math Fair Topic

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### Cereal Box Volume and Surface Area Math Fair Topic

Does this experiment make sense?

Cereal Box Geometry

The purpose is to measure the dimensions of different sized cereal boxes to figure out which brand has the most volume of cereal in the least amount of packaging or surface area.

Hypothesis: If the surface area of one cereal box is greater than another, then it should contain more cereal.

Procedures:

1. Create a data table in my notebook to keep track of my results. The table will include the name brand of the cereal, the length, width, and height of the cereal box in inches, the surface area in square inches, and the calculated volume in cubic inches.

2. Measure the length, width, and height of each cereal box in inches with a ruler and record in my notebook. Repeat this process two more times.

3. Calculate the surface area and volume using the formulas below (l = length in in., w = width in in., h = height in in.).

a. Surface area (in.2) = 2lh + 2wh + 2lw

b. Volume (in.3) = lwh

4. Record the formula results in my notebook in the data table.

Cereal Box Geometry

The purpose is to measure the dimensions of different sized cereal boxes to figure out which brand has the most volume of cereal in the least amount of packaging or surface area.

Hypothesis: If the surface area of one cereal box is greater than another, then it should contain more cereal.

Procedures:

1. Create a data table in my notebook to keep track of my results. The table will include the name brand of the cereal, the length, width, and height of the cereal box in inches, the surface area in square inches, and the calculated volume in cubic inches.

2. Measure the length, width, and height of each cereal box in inches with a ruler and record in my notebook. Repeat this process two more times.

3. Calculate the surface area and volume using the formulas below (l = length in in., w = width in in., h = height in in.).

a. Surface area (in.2) = 2lh + 2wh + 2lw

b. Volume (in.3) = lwh

4. Record the formula results in my notebook in the data table.

### Re: Cereal Box Volume and Surface Area Math Fair Topic

Hi jwaber,

Your experiment sounds like it is off to a good start. An experiment that Science Buddies has that is pretty similar is linked below to help as you continue with your experiment:

https://www.sciencebuddies.org/science- ... x-geometry

I hope this helps and feel free to reach out with any more questions,

Lili

Your experiment sounds like it is off to a good start. An experiment that Science Buddies has that is pretty similar is linked below to help as you continue with your experiment:

https://www.sciencebuddies.org/science- ... x-geometry

I hope this helps and feel free to reach out with any more questions,

Lili

### Re: Cereal Box Volume and Surface Area Math Fair Topic

One of my children is doing that experiment. To change it up for the other, I used cereal boxes. The problem is that cereal is reported by weight, so the experiment is not as complex as with juice boxes. Adding the weight element is too advanced for my child's age. For cereal, we have to stop at the calculated SA and Volume comparison. There is no actual volume.

### Re: Cereal Box Volume and Surface Area Math Fair Topic

Hi jwaber,

If you want to follow the same procedure as what you would with the juice box, maybe you could use different ice cream brands and determine what ice cream brand has the most volume in the least amount of packaging space. Using ice cream instead of the cereal will allow you to calculate the volume like you would with the juice boxes and you wouldn't have to worry about weight.

Hope this helps,

Lili

If you want to follow the same procedure as what you would with the juice box, maybe you could use different ice cream brands and determine what ice cream brand has the most volume in the least amount of packaging space. Using ice cream instead of the cereal will allow you to calculate the volume like you would with the juice boxes and you wouldn't have to worry about weight.

Hope this helps,

Lili

### Re: Cereal Box Volume and Surface Area Math Fair Topic

For the juice box experiment, what is the conclusion? How do we know that the box with the greatest surface area and calculated volume holds the most juice if the test samples list the same fl. oz.? One has a greater SA and V, therefore more wasted packaging, yet we don't know if the box holds more juice than that of the box with the same listed fl. oz. unless we believe in geometry.

### Re: Cereal Box Volume and Surface Area Math Fair Topic

The aim of the experiment is to determine which brand gives the most juice in the least amount of packaging. Therefore, the conclusion will describe the ratios of volume to surface area of each brand and the brand that has the closest 1:1 relationship will be the brand that maximized the amount of juice sold in the least amount of packaging.

Hope this helps,

Lili

Hope this helps,

Lili

### Re: Cereal Box Volume and Surface Area Math Fair Topic

Volume in cubic inches and surface area in squared inches?

### Re: Cereal Box Volume and Surface Area Math Fair Topic

What is the hypothesis if you go down the road of using SA/V as a conclusion? What were you trying to prove?

### Re: Cereal Box Volume and Surface Area Math Fair Topic

Yes, the volume would be measured in cubic inches, while the surface area would be squared inches.

The hypothesis for the surface area to volume would include making an inference as to what brand will have a surface area to volume ratio that is closest to 1 to 1. The inference does not have to be correct and it may help to consider which cereal box (or whatever food item you are using) has the least amount of empty space on top.

If the ratio of a brand is close to 1:1, that means that the brand has efficiently used all of the packaging to contain the most amount of food that it can hold. Therefore, the brand with the ratio closest to 1:1 will have used the most effective amount of packaging when selling its product, making it the "winner" of the experiment.

Hope this helps,

Lili

The hypothesis for the surface area to volume would include making an inference as to what brand will have a surface area to volume ratio that is closest to 1 to 1. The inference does not have to be correct and it may help to consider which cereal box (or whatever food item you are using) has the least amount of empty space on top.

If the ratio of a brand is close to 1:1, that means that the brand has efficiently used all of the packaging to contain the most amount of food that it can hold. Therefore, the brand with the ratio closest to 1:1 will have used the most effective amount of packaging when selling its product, making it the "winner" of the experiment.

Hope this helps,

Lili