Chapter 1: Q42. (page 19)

A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

Short Answer

Expert verified

The average diameter of a single alveolus is 0.234 mm.

Step by step solution

Step 1. Volume of a sphere

The volume of a sphere can be calculated using its radius. Both these values are directly related to each other. Hence, as the radius increases, the volume of the sphere also increases.

Step 2. Calculation of the volume of alveolus

Assume that the alveoli are spherical, and the volume of a typical human lung is about 2.05 liters.

Given that there are 300 million alveoli per lung.

So, the volume of a single alveolus is:

$\begin{matrix} V = (\frac{2.05 liters}{lung}) (\frac{1 lung}{3 \times 10^{8} alveoli}) \\ = (6.833 \times 10^{- 9} \frac{liters}{alveolus}) (\frac{10^{6} {mm}^{3}}{1 liter}) \\ = 6.833 \times 10^{- 3} \frac{{mm}^{3}}{alveolus} \end{matrix}$

Step 3. Calculation of the radius and diameter of a single alveolus

The radius of a single alveolus can be calculated as:

$\begin{matrix} V = \frac{4}{3} π r^{3} \\ (6.833 \times 10^{- 3} {mm}^{3}) = \frac{4}{3} π r^{3} \\ r = 0.117 mm \end{matrix}$

The average diameter of a single alveolus can be calculated as:

$\begin{matrix} d = 2 r \\ d = 2 (0.117 mm) \\ d = 0.234 mm \end{matrix}$

Thus, the average diameter of a single alveolus is $0.234 mm$ .

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A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

Short Answer

Step by step solution

Step 1. Volume of a sphere

Step 2. Calculation of the volume of alveolus

Step 3. Calculation of the radius and diameter of a single alveolus

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