How big are your lungs?

Geometry Level 4

Both of our lungs are covered by thin membranes called pleura. The surface area of such overlying layer is about 1,000 $\text{ cm}^{2}$ per each lung.

Nevertheless, deep inside, the lungs contain numerous grape-like clusters of microscopic spherical sub-units, called alveoli, where the gas exchange takes place, and each alveolus has a diameter of about 200 microns. (1 micron = $10^{-6}$ meter)

If there are averagely 600 million alveoli in normal adult lungs, approximately, how many times is the lungs' internal surface area larger than the external one? (Round the answer to the nearest hundreds.)

600 1600 200 400 100 800

1 solution

Worranat Pakornrat
Nov 5, 2015

To calculate the internal surface area of the lungs, we need to find the surface area of each alveolus first. One alveolus has a diameter of 200 microns, so its radius = 100 microns = $100\times(10^{-6}$ ) meter = $10^{-4}$ meter.

The surface area of a sphere = 4 π $r^{2}$ ≈ $12.57\times(10^{-8}$ ) $m^{2}$

There are 600 million alveoli, so the total internal surface area = (600,000,000)( $12.57\times(10^{-8}$ ))

= $6 \times 12.57$ ≈ 75.42 $m^{2}$ [Yes, your lungs have a size of a tennis court!]

The outer surface area of pleura = $2\times1,000$ $cm^{2}$ (Remember there are 2 lungs.) = 2,000 $cm^{2}$ = 0.2 $m^{2}$

Therefore, the ratio of the internal surface area to the external one = 75.42/0.2 ≈ 377.1

Thus, the nearest answer is 400 times. In plain words, your lungs are about 400 times larger than they look!

How big are your lungs?

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