Breast Size Measurement via Archimedes’ Principle

Breasts come in a wide variety of sizes, and due to their shape, are difficult to accurately measure to determine their actual sizes. In this study we will use Archimedes’ Principle, which uses the displacement of water, to measure the sizes of both natural breasts and augmented breasts.

Initial observation:
By visual inspection, breasts naturally occur in a variety of sizes.

Question:
Since many breasts are not easily modeled using simple geometric shapes, estimating volumes can be difficult. Can Archimedes’ principle be used to measure the actual volume a breast?

Expectation:
Some measurable variation in volume is expected. In particular augmented breasts are expected to be generally larger than natural breasts.

Equipment & Materials:

Procedure:
Before measuring the volumes of each breast, an attempt to mass each breast was also made. For the sake of brevity, the procedure for massing breasts is not given.

  1. Place the smaller bowl inside the larger one, preferably such that the smaller bowl is easily removable (we had to rest the smaller bowl on an empty tin can, see the apparatus below).
  2. Fill the smaller bowl all the way to the very top, being careful not to spill any water into the larger bowl.
  3. Gently lower a single breast into the smaller bowl, displacing water (try to prevent any splashing or sloshing).
  4. Run out into street yelling “Eureka, Eureka!” (optional)
  5. Remove breast from water.
  6. Remove smaller bowl (and in our case, the tin can).
  7. Place an empty measuring cup onto the kitchen scale and zero the scale.
  8. Pour water from larger bowl into the measuring cup on the kitchen scale to mass the displaced water (we will assume the water has a density of 1 gram per milliliter).
  9. Repeat steps 1 through 8 with all available breasts.

Data:
For this experiment, we were able to acquire three types of breast, these included natural, amish, and augmented. Before we started taking measurements, we took a group photo showing all of the breasts together.

To perform the displacement portion of the experiment, we used an apparatus made using two bowls and a large tin can, as shown below. Due to the size of the augmented breasts (see surprise observation below), we were initially concerned that the upper bowl might not be large enough, but our concerns were unfounded.

Breast measuring apparatus based on Archimedes' principle.

Breast measuring apparatus based on Archimedes’ principle.

The measurements of all available breasts are given in the following table.

Mass (g) Volume (mL) Density (g/mL)
Natural 165.0 96.4 1.71
165.9 99.7 1.66
173.4 136.5 1.27
Amish 166.0 118.2 1.40
156.7 101.1 1.55
139.3 97.6 1.43
Augmented 416.7 375.0 1.11
309.9 261.2 1.19
289.6 221.9 1.31

When plotted, the volume of each breast does have a fairly linear relationship with the mass of the breast, as show in the graph below.

Breast volume vs. breast mass.

Breast volume vs. breast mass.

To examine the relationship between size and density, the density versus mass is plotted below.

Breast Density

Breast density vs. breast mass.

The general downward trend of density as mass increases is interesting. However even the largest breasts measured still had a density greater than 1 g/mL, and therefore still sink in water.

Surprise Observation:
The shear size of the augmented breasts was mind boggling. For comparison here are pictures of the unaugmented breasts and augmented breasts with equally sized grids for size comparison.

Conclusion:
Archimedes’ Principle, does seem to be an effective way of measuring the volume of breasts. As expected, augmented breasts were measurably larger in terms of both mass and volume. Also, more massive breasts tended to have larger volumes as well. Somewhat surprising however is that density tends to decrease as mass increases.

Future Questions:
In the density vs. mass graph there is a downward trend, in future studies it would be interesting to look at extremely large breasts to see if they achieve a density less than 1g/mL and would therefore float on water. Additionally examining at a set of breasts both before and after augmentation to determine what affect the actual augmentation process has on both mass and volume.

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2 thoughts on “Breast Size Measurement via Archimedes’ Principle

  1. Pingback: Qualitative assessment of chicken breasts | Doing Science To Stuff

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