don’t check the math

Some people might look at a colossal stadium such as the Superdome and see only the number of seats available (up to 72,003 for football games). While that number is impressive, I can’t help but wonder how many people could actually fit in there if the stadium were filled to its maximum capacity – that is, by stacking people on top of each other to fill the entirety of its volume. One could argue the practicality of such an endeavor, but that’s really a moot issue to me. For those who would like to know how many people the New Orleans Superdome could hold, I’ve got you covered.

First of all, what’s the volume of the average person? Well, this can be approximated by treating a human like a cylinder and proposing an average height of 170 cm (~5.6 feet) for American males and females. The average shoulder width, if I had to guess (and I do), would be about 53 cm (21 inches), and this is probably the maximum diameter needed (excluding really fat, or really buff, people who don’t compress easily). So our person looks like this:

guy.jpg

Now, the volume of our cylinder (and this is generous to compensate for fat people and to leave a little bit of excess room for excrement) is (pi)r^2h, so it’s 3.14(26.5^2)170 or 375,051.19 cm^3. We know from this document (warning: PDF link) that the volume of the Superdome is 4.6 million cubic yards. If one cubic yard is 764,554.84 cm^3 (thanks Waldo), then the volume of the Superdome is 4.6e6(764555) or 3.517e12 cm^3. Dividing this by the average human volume yields a total capacity of 9,377,259 people (plus almost another third of a person). That’s only about 3% of the U.S. population, but that’s not too shabby.

But wait, there’s more! How many babies could fit in the Superdome? If the average length of a newborn infant is 47.4 cm (see here), and the average head width (roughly the same as the shoulder width, for the diameter) is ~9.6 cm, then the baby’s volume is 3431 cm^3. That would suggest that you could stuff an impressive 1,025,051,880 babies in there. Just so you know.

4 thoughts on “don’t check the math

  1. Thanks Susan. I entered the radius and height of our human and it agreed with our human volume.

    I think I’d still like to do it the old fashioned way if I had it to do over again.

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