Thank you to everyone who entered our Fermi Estimation Contest this past January. Congratulations to winner Alex D, who received a free copy of *How Many Licks?* Several contestants asked for my solution, so I’m posting my results below:

**Problem:**

How many snowflakes are in this snowman?

**Solution:**

I assumed the snowman was made of three spheres of radii R_{1}=30 cm, R_{2}=45 cm, and R_{3}=65 cm. The volume of the snowman is then given by:

V = (4Pi / 3)*(R_{1}^{3} + R_{2}^{3}+R_{3}^{3}) ~ 1.6m^{3}

From Hypertextbook.com, there are roughly 100 crystals per snowflake and 10^{18} molecules per crystal. One water molecule weighs 2.992x10^{-26} kg. From these facts, we can calculate the mass of a flake:

(100 crystals per flake)

*(10^{18} molecules per crystal)

*(2.992x10^{-26} kg per molecule)

-----------------------------------

3.0x10^{6} kg per snowflake

According to Wikipedia, the density of snow varies considerably from 8% the weight of water for newly fallen snow, to 30% after it settles, to 50% in late spring. Since the density of water is about 1000kg/m^{3} and the snowman is pretty densely packed, I chose 500 kg/m^{3}.

Using these numbers, we can calculate the number of snowflakes:

(1.6 m^{3})*(500 kg per m^{3}) / (3.0x10^{6} kg per snowflake) ~ 2.7x10^{8} snowflakes

## No comments:

## Post a Comment