Given that the diameter of the egg is \(100 \, \mu m\), the radius \(r\) is half of the diameter:

\[
r = \frac{100 \, \mu m}{2} = 50 \, \mu m
\]

Now, using the formula for the volume of a sphere:

\[
V = \frac{4}{3} \times 3.14 \times r^3
\]

Substituting the value of \(r = 50 \, \mu m\):

\[
V = \frac{4}{3} \times 3.14 \times (50 \, \mu m)^3
\]

Now let's calculate this.

\[
V = \frac{4}{3} \times 3.14 \times 125000 \, \mu m^3
\]

\[
V = \frac{4}{3} \times 392500 \, \mu m^3
\]

\[
V = 523333.33 \, \mu m^3
\]

So, the volume of the egg is approximately \(523,333.33 \, \mu m^3\).

Would you like more details on this, or do you have any other questions?

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**Relative Questions:**
1. How does the volume of an egg compare to that of a perfect sphere with the same diameter?
2. What is the formula for the volume of an ellipsoid, which is more accurate for an egg's shape?
3. How does changing the radius affect the volume of a sphere?
4. Can you derive the formula for the volume of a sphere from basic principles?
5. What would the volume be if the diameter were doubled?
6. How would you calculate the surface area of this egg?
7. What is the significance of using \(\pi\) in volume calculations?
8. How does the volume calculation change if we used a different unit of measurement?

**Tip:** Always double-check your unit conversions, especially when working with very small or very large measurements.

Learn how to calculate the volume of an egg with a diameter of 100 micrometers using the formula for the volume of a sphere. Detailed step-by-step solution provided. Suitable for high school students studying geometry and sphere volume calculations.

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