# Volume and surface area of Human Body, World Population of Living Matter

When doctors see patients, they almost always take two measurements first: height and weight. Yes, they want to track their patient’s progress but more importantly, they need to understand the patient’s volume and surface area for prescribing medicine.

If you're an average human being, the density of your body is about 8.3 lbs/gal., which is a little less than seawater but a little more than pure water. So first we divide your weight in pounds by 8.3 to find out the number of gallons you make up. Since the number of gallons per cubic foot is 7.58 gal/ft.^3, we divide your total gallons by 7.58. For example, Mr. Kramer weights about 160 lbs. so my gallons are 160/8.3 = 19.28 gal. and when we divide 19.28/7.58 = 2.54 ft.^3. So if you liquified my volume, I could fill a little more than two and a half cubic feet.

I had the children calculate their cubic feet using the calculators after they first estimated their liquified volume. Then they wrote down everyone in their family, friends, pets (animals have similar densities to humans), etc. to test during the week. Asking someone for their weight is easy if you give it context: “I am doing a math/science experiment to determine the cubic feet of humans. Would you like to participate?”

We also determined the volume of the average human of 110 pounds to be 1.74 ft.^3 and multiplied this by the world population of 7.5 billion to get about 13 billion ft.^3. I showed them (page 4 of their pdfs), what such a cube would look like superimposed in New York City. It would only be 1007 meters in dimension cubed and cover a small portion of lower Manhattan. I even showed how the tallest building in the world, the Burj Khalifa, in Dubai, and the Empire State Building would look in comparison to total world population cube.

I then had the children make conjectures about how the human population volume would compare to other volumes of plants, insects, fish, even bacteria. Most thought that these other living organisms would be greater than humans but then I showed them an actual comparison and they were astounded. Plants which comprise 450 gigaton of volume is 7,500 times larger than the human volume. Even insects are close to 17 times our volume. So, they concluded that humans are quite insignificant in volume but such high impact on these other living organisms. Humans have quite the responsibility they concluded.

I had them calculate the cubic footage of the largest animals such as the blue whale, whale shark, elephants, and so on.

Finally, for the older children, we looked at Mollester’s formula for calculating the Body Surface Area (BSA) in square meters and square feet. This is another calculation doctors use to administer medicine. The children and I imagined that a steamroller were to flatten us out. How much area would our skin take up? In class, I had a square meter for them to make these conjectures. The calculation is on page 6 of the pdf and you will see an example of my BSA showing 1.87 m^2 and 20.16 ft.^2. The calculation requires both weight and height, each of which you have to convert to kilograms and centimeters, respectively. The conversion from pounds to kilograms is to divide by 2.2 and the conversion from inches to centimeters is to multiply by 2.54. Of course, calculators are necessary for the BSA and a lot of careful recording.

Have fun with human volume and surface area and respect your doctors, they are some of the great mathematicians.

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Volume_and_Surface_Area_of_Human_Body_World_Population_of_all_Living_Matter.pdf10.29 MB