How many lacrosse balls will it take to fill the Atlantic Ocean

1.  Background Story: 

 Have you ever wondered how big a lacrosse ball is? My question is how many lacrosse balls will it take to fit in the Atlantic Ocean. I chose this question because I really like lacrosse and it seems like it will be cool to see a comparison how big the Atlantic Ocean is. 

2.  Ask Yourself This: .

What's the volume of the Atlantic Ocean?

How many cubed inches will a lacrosse ball take up?

How will I fill the space in between balls because they are round they will not stack up. 

3.  Helpful Hints:  

.

3 x 10^20L that's how many liters of water. About 320 million cubic kilometers. Or 80 million cubic miles. 

3.20000000

8 places 

3.2x10^8

http://oceanservice.noaa.gov/facts/atlantic.html

http://www.reefnews.com/reefnews/infopage/oceans/ocean.html

.

a lacrosse ball is about 2’’ around and 2’’ tall and when they stack up, there will be a space in between the balls that will not be filled. It will not be filled because when you stack up lacrosse balls, they are round so there is space in between.

4.  Construct a Formula: .

Diameter .times half mile times those balls acrosse times miles up 

You multiply by half mile because each ball is two inches so if you multiply by half mile you'd get a mile long line of lacrosse balls. 

What I will do in order to find out how many lacrosse balls will fit into the Atlantic Ocean is find out how many miles cubed the Atlantic Ocean is, then I'll find out how many lacrosse balls will fit into one cubic mile. Then multiply that number by how many cubic miles there is in the Atlantic Ocean. Which will get you to the answer. 

5.  Messy Math: .

2"x2640'x2640'x8x10^6m=1115136x10^8 lacrosse balls. 

(Need to include all your units here - scientific notation?)

6.  Answer:  

There is about 1115136x10^8 lacrosse balls. And that's not including all the space in between the balls that's not filled up. Imagine how many it would be if you filled the space between balls

How many light are in all the schools in Vermont?

 


1.  Background Story:

For my Fermi problem I have decided to do it on, how many lights are in all the schools in Vermont? I got interested in this question because I was curious about how many lights were in Harwood but it would be too small of a number and I could just count, though it would take awhile. So Mr. Wagner told me that I should research how many light were in all the middle and high schools in Vermont.


2.  Ask Yourself This:

How many schools are in Washington county?

How many counties are in Vermont?

How many lights per class room?

How many class rooms are in a middle/high school?

3.  Helpful Hints:

Question 1 Answer; there are 21 schools in Washington county.
http://www.greatschools.org/schools/districts/Vermont/VT

Question 2 Answer; there are 14 counties in Vermont.
 http://www.greatschools.org/schools/districts/Vermont/VT

Question 3 Answer; there approximately 54 class rooms in middle/high schools

Question 3 Answer; I think that that there is about 20-36 light per class room because I counted how many lights were in 4 of the core class rooms and got a number between 20 & 36.


4.  Construct a Formula:

                   lights  *   class rooms *  schools  *  counties  =  lights
            classrooms      schools    counties     Vermont   Vermont

5.  Messy Math:

   36 Lights   *  54 CR*   21 S *  14 C =    571,536 lights
      1 CR            1 S       1 C     1 VT              1 VT


6.  Answer:
 There are approximately 571,536 lights in all the middle and high school class rooms in Vermont together.

If all the trees in Vermont were cut down, how much 11 by 8 1/2 inchpaper could be made?

Vermont being a very mountainous and fertile place, has many trees. Maria and Stephen were outside on a walk up the mountain and were flabbergasted by the amount of trees they could see when the got to the top. This made them think, if all the trees in Vermont were cut down then how much 11x81/2 paper could be made?

How many trees are in Vermont? How many trees does it take to make 11x81/2 paper? What kind of trees provide what kind of paper amount? Tree sizes? How many acres are in Vermont?

1) 187 trees per acre in Vermont.

(http://www.vtfpr.org/util/for_utilize_stats.cfm)

2) One tree produces 80,500 pieces of printer paper (11x81/2).

(http://science.howstuffworks.com/environmental/green-science/question16.htm)

3)To make this a somewhat easy test I am going to say that every tree produces the same amount of paper.

(The website I used to find paper per tree is in helpful hint 3)

4) Since trees vary in sizes I am going to use the normal size tree, an adult tree.

(This is the size of the tree that is used to get 80,500 pieces of paper, "Most are about 1 foot in diameter and 60 feet tall. Ignoring taper, that's about 81,430 cubic inches of wood:" I used the same website as the one in helpful hint 2)

5) There are 6,158,607 acres in Vermont.

(http://wiki.answers.com/Q/How_many_acres_is_in_.97_acres#page1) 

One Pine tree produces 80,500 pieces of 11x81/2 inch paper. Since there are a variety of trees in Vermont, I am going to assume that all of the trees are pines.

To find the answer, you need to know how many trees are in an acre and how many acres are in Vermont. You also need to know how much paper a single tree produces. When you have this information you first want to find out how much paper is made per acre. To find this you multiply the number of trees per acre by the amount of paper produced by a single tree. Once you know how much paper is made per acre, you want to multiply that by how many acres are in Vermont. Then you will have your answer in paper/Vermonts total acres. 

If one tree produces 80,500 pieces of 11 x 81/2 paper and they are 187 trees in 1 acre than 1.50535 x 10^7 pieces of 11x81/2 paper are produced in one acre. There are 6.158607 x 10^6 acres in Vermont so if there are 1.50535 x 10^7 pieces of paper per acre then in Vermont, if you used all the trees to make paper then, you would get 9.270859 x 10^13 pieces of paper made from ally he trees in Vermont.

80,500 x 187 = 1.50535 x 10^7 pieces of paper per acre

1.50535 x 10^6 x 6.158607 x 10^7 = 9.270859 x 10^13 pieces of paper in Vermont

That is equal to 92,708,590,000,000,000,000 which is also equal to 185,417,180,000,000,000 reams of paper (500 papers per ream)

By using the fermi method, I predicted how much 11x81/2 could be made from all the trees in Vermont. My prediction is that if all the trees in Vermont were cut down to make paper, you could make 92,708,590,000,000,000,000 pieces of printer paper. (Shown in #5)

How many grains of sand are in the Sahara Desert?

1.  Background Story:

 I chose to do how many grains of sand are in the Sahara desert because I wanted to do one that would come out with a really big complicated number.




2.  Ask Yourself This:

I'm doing like more of a layer, like a blanket of sand over the Sahara desert so I don't have to do the volume.

how many square miles are in the Sahara desert.

 How many grains of sand are in a square foot

 How many square feet are in a square mile



3.  Helpful Hints:


how many square miles are in the Sahara desert: 3.629 million sq miles (9.4 million km²)

How many grains of sand are in a square foot: 45,000

 How many square feet are in a square mile: 27,878,400 square feet


I rounded the numbers to make them more simple. And I also didn't do the depth of the sand so there Is probably more sand then what my information would allow you to get. But for the layer of sand over the Sahara there are 4.51926632x10^16





4.  Construct a Formula:
Amount of grains of sand per square foot X how many square miles are in the Sahara X how many square miles are in the Sahara desert.

How long would it take two rats to fill up Lake Superior with rats?

Background Story:  

It is a fairly common saying: breeding like rats. Or, multiplying like rats. One day after hearing this saying, I wondered, "How fast would two rats take to breed enough to fill up a swimming pool with rats?" I decided to expand this into the fermi problem:How long would two adult brown rats take to breed enough to fill up Lake Superior, if they had an unlimited supply of food and water?(I also assumed that there was only one breeding pair of rats at a time.) My reason for choosing brown rats is because they are the most widespread species of rats. 

Ask Yourself This:  

How long is a brown rat's life span?

How long does it take a brown rat to mature enough to breed?

How long is a brown rat's breeding cycle (how long between litters)

How large is an average brown rat litter?

What is the volume of an average brown rat?

What is the volume of Lake Superior?

Helpful Hints:  

a.  

Rat data

Data from http://animaldiversity.ummz.umich.edu/accounts/Rattus_norvegicus/

Gestation period: about 23 days

Males usually reach sexual maturity at 3-4 months

Females usually reach sexual maturity at 3-4 months

Around 18 hours after giving birth, the female mates again

Typical lifespan: 2-3 years (30 months)

Number of rats per litter: about 8

Data from:http://www.arkive.org/brown-rat/rattus-norvegicus/ 

Head/body length of a brown rat: 20-28 cm

Tail length:17-23 cm

Data from:http://www.epa.gov/greatlakes/factsheet.html 

Lake Superior info

Volume: About 23,000 cubic km 

b.  

Length between  brown rat litters: 23.75 days

23 days = 552 hrs   552 hrs + 18 hrs = 570 hrs

570 hrs/ 24 hrs= 23.75 days

Volume of a brown rat: 2646 cubic cm

I estimated based on a diagram that the ratio of height to body length is about 3.5:8, and that the height and width were about the same. Since the  body length is about 24 cm, and 24 cm is 8 x 3, I multiplied 3.5(height in the ratio of height to body length) by 3 to get 10.5 cm, which is the height of an average brown rat. Then, I multiplied length and height to get 252 square cm for the area. I multiplied that by the width to get 2646 cubic cm.

Construct a Formula:  

First, I’ll have to divide the volume of Lake Superior by the volume of each rat, to find out how many rats we need to fill it up. Next I’ll divide the rat’s life span(minus 3.5 months) by the length between litters, to find the # of times 2 rats can mate in their lifetimes. Then I’ll have to multiply that # by the # of rats per litter, to find how many babies those rats make in their lifetimes. Then I’ll divide the number of rats it takes to fill up Lake Superior by that number, to find how many rat life spans it will take to fill up Lake Superior. 

Since each rat lifespan is 2.5 years, I’ll multiply that # by 2.5. Along the way, I’ll also have to exchange the units.

*

Sorry if this is a little faint.

Messy Math:  

*

Again, sorry if this is a little faint. Also, I kind of had a hard time doing the last part in fractions.

Answer:  

If two brown rats had an unlimited amount of food and water, it would take them about 2.15x10^23 years to fill up Lake Superior with rats.

If you stacked all the sheets of homework one middle schooler does in one year, how tall would the pile be?

Everybody knows that a piece of paper isn't thick at all but can something so thin add up over time? This is one of the things that will hopefully be answered in my fermi problemy. My questions is if you stacked all the homework papers that one harwood eighth grader gets in one school year how tall would the stack be? I chose this question because I often hear kids saying "I have piles of work to do"  Is this just people being dramatic or is there some truth this? I want to know how much homework do we do every year.

To find the answer to my problem I must first answer the following questions.

How thick is the average piece of paper?

On average how many sheets of homework does the average harwood middle school student get each night?

How long is our school year?

I know that 500 sheets of papers makes an inch. I learned that harwood school year is 170 days. From Ms. Curren I learned that the average 8th grader gets 2-3 pages of homework each night. I estimate that 2 to 3 pages is about 2.5 pages. If I calculate the thickness of a sheet of paper by dividing  an inch by 500 (papers) it would come out to be 0.002 . My sources were Mrs. Current, Mrs Therrein and mathforum.org.

 To solve this in  a mathematical formula first I would put all of my data into fractions. The fractions should be set up so that I end with the amount of pages over one year

How many elephants would fit into the Empire State building

Name __Wesley Lowe________________________________________

1.  Background Story:

My Fermi problem is, how many elephants can fit into the Empire State Building. I chose this problem because it has many variables to test. The variables are, how old is the elephant, and is it a boy or girl.

2.  Ask Yourself This:

How many square feet are there in one floor of the Empire State Building? How many floors are there in the Empire State Building? What is the average size of an adult elephant?

3.  Helpful Hints:

there are 102 Floors in the Empire State Building. There is exactly 2,768,591 square feet of usable space in the empire state building. The average size of a female African elephant is cubic feet  is 176 square feet.

4.  Construct a Formula:

multiply the amount of elephants by the average size of one floor, and then you multiply that number by the amount of floors.

5.  Messy Math:  

2,768,591 square feet in the empire state building divided by 102 floors= 27,143 square feet in one floor of the empire state building.

27,143 square feet in one floor divided by 170 square feet in one elephant= 159 elephants, per floor.

159 elephants multiplied by 102 floors= 16,218 elephants fit in the empire state building.

6.  Answer:  

The answer to my problem (how many elephants would fit into the empire state building?) is approximately 16,218 average size female elephants.