Consider a cylindrical baby


Now with 30% more baby (by weight)!

At birth, Stellan weighed 7 pounds, 3 ounces, and was 19.5 inches long (At some point the “height” dimension will replace “length,” which will later take on another meaning entirely, but we have not yet reached that point.) As of his latest pediatric appointment two days ago, he weighed 9 pounds 1.5 ounces, and had grown to 22 inches long.

It’s difficult if not impossible to obtain an accurate measure of the volumetric area of a baby: all babies hate Archimedes and deeply resent displacement by immersion; this is a well-documented fact. Fortunately, we can make a rough estimate by assuming a cylindrical baby, using the circumference of the head measured at birth as 34 cm, and currently at 36 cm. (Why the maternity nurse chose to switch units for length vs circumference is unknown to me. We’ll continue in metric, because it’s classier.) This will be a maximal estimate, as the head is — memorably, to anyone present in the delivery room — the largest-diameter portion of the human body, but it’s good enough for our purposes. Anyway, it’s all we’ve got.

[Incidentally, and I forgot to mention this before: by most measurements Stellan is close to or slightly larger than average; his head circumference, however, is in the bottom 10%. Meaning that either my son has a teeny-tiny brain, or a large portion of the world is populated primarily by bobblehead dolls.]

A little half-remembered geometry, and Google, tells us that the volume of a cylindrical baby with circumference c and length l is (c2l) / (4π), giving us an at-birth volume of 4,554 cm3 and a present-day volume of 5,827 cm3.

From this we can easily deduce that the density of our baby has remained constant from birth to the present day, at roughly 0.72 grams per cubic centimeter (or if you prefer 0.025 pounds per cubic inch, or 0.4 ounces per cubic inch). This is reassuring, as any non-constant trend in density could have unfortunate implications for our son’s future buoyancy.