How many soccer balls could fit in lake Champlain?

1.  Background Story:

   A Fermi problem helps figure out a fast estimate of a quantity for something very large or small. My Fermi question was: How many soccer balls could fit in Lake Champlain? I chose this problem because I thought this would be a challenging problem to figure out. It took a lot of area and volume work to figure the problem out. I also like soccer and spend a lot of time on Lake Champlain, so I think it is a good problem for me.

2.  Ask Yourself This:  

How many sq. mi. is Lake Champlain?

What is the radius of a size 5 soccer ball?

How much space is between the balls?

What is the average depth of Lake Camplain?

3.  Helpful Hints:  

Lake Champlain is 490 sq. mi. (Google)

Radius of a size 5 soccer ball is 4.5 in. (football-bible.com)

17.4in. Left open from every square space the ball takes up.

The average depth of Lake Champlain is 64ft. (historiclakes.org)

Sometimes the balls will align in a triangle so I am going to estamate the space in between each ball is about 5sq. in. That is about 1/6 of the square space of the ball.

4.  Construct a Formula: 

I would find out how many sq. mi. there are in Lake Champlain. Then how many sq. ft. in a sq. mi.. After that I would find how many sq. in. in a sq. ft.. Lastly I would find out how many sq. in. are in Lake Champlain

Later I will multiplay the surface area(in) by the depth(in) to find the volume of Lake Camplain(in).

5.  Messy Math:  

6.  Answer:  

2x10^12 soccer balls

If you were to line all of those up you could go around the earth 11,000 times.