A person has 400 million alveoli per lung with an average radius of 0.1 mm for each alveolus. Considering the alveoli are spherical in shape, the total respiratory surface of that person is closest to

Options

A. `500" "mm^(2)`
B. `200" "mm^(2)`
C. `100" "mm^(2)`
D. `1000" "mm^(2)`

Explanation

To find the total respiratory surface area of the alveoli in a person's lungs, we can follow these steps:

### Step 1: Understand the shape and formula for surface area
Alveoli are spherical in shape. The formula for the surface area \( A \) of a sphere is given by:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

### Step 2: Calculate the surface area of one alveolus
Given that the average radius \( r \) of each alveolus is 0.1 mm (which is 0.0001 m for calculations in standard SI units), we can substitute this value into the surface area formula:
\[ A = 4\pi (0.0001)^2 \]
Calculating this:
\[ A = 4\pi (0.00000001) = 4\pi \times 10^{-8} \text{ m}^2 \]
Using \( \pi \approx 3.14 \):
\[ A \approx 4 \times 3.14 \times 10^{-8} \approx 1.256 \times 10^{-7} \text{ m}^2 \]

### Step 3: Calculate the total surface area for all alveoli in one lung
The total number of alveoli per lung is given as 400 million, which is \( 400 \times 10^6 \). Therefore, the total surface area \( A_{total} \) for one lung is:
\[ A_{total} = 400 \times 10^6 \times 1.256 \times 10^{-7} \text{ m}^2 \]
Calculating this:
\[ A_{total} \approx 400 \times 1.256 \times 10^{-1} = 50.24 \text{ m}^2 \]

### Step 4: Calculate the total surface area for both lungs
Since the question refers to the total respiratory surface area for both lungs, we multiply the surface area of one lung by 2:
\[ A_{both} = 2 \times 50.24 \text{ m}^2 = 100.48 \text{ m}^2 \]

### Step 5: Round to the nearest value
The total respiratory surface area of that person is closest to:
\[ \approx 100 \text{ m}^2 \]

### Final Answer
The total respiratory surface of that person is closest to **100 m²**.

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