The following questions and estimated solutions are presented by 8th graders at Harwood Union Middle School in honor of Enrico Fermi. The blog is inspired by a modern day Fermi geek, Dr. Aaron Santos, who writes his own blog, A Diary of Numbers. Check out his link in the side bar.
Monday, October 28, 2013
How Much Money Would It Cost to Cover the Empire State Building withPrinter Paper
How much money would it cost to cover the Empire State Building with sheets of printer paper?
I was stuck thinking about what to do for my fermi problem. I’ve always been interested in tall buildings. All the hard work and time it takes to make massive building always catches my interest. The tallest buildings stretch from the Empire State Building at 381 meters to Burj Khalifa at 828 meters into the clouds. I have chosen the Empire State Building for a building because of the fact its located right near us in New York City. I have chosen printer paper as another variable because of its rectangular shape.
What are the dimensions of the Empire State Building?
What is the dimension of a piece of printer paper?
How many floors are in the Empire State Building?
Empire State Building
Width: 187 feet
Length: 424 feet
Height: 1,454 feet
http://tallest-buildings.findthedata.org/l/57/Empire-State-Building
Printer Paper
length: 11 inches
Width: 8.5 inches
http://www.dpandi.com/paper/
500 sheets of printer paper ≈ 7.50
7.50 / 500 = .015
Each piece of printer paper costs about .015
To find out how many sheets of paper can fit along the outside of the Empire State Building I will have to find the Surface area of one side of the building by multiplying the length with the width and the hieght. Then I will find the entire surface area by multiply the answer by 4 . This number is only the surface area of the sides of the Empire State Building. I will find the surface area of the top by multiplying the width by the width. Once we have the surface area of the building we will need to calculate how many square inches the surface area is by dividing the number of square feet by 12. This step is so that I can figure out how many pieces of paper will fit on the surface area of the Empire State Building. Next find the surface area of a piece of printer paper by multiplying the length multiplied by the height. After that step I can find out how many pieces of printer paper will fit along the surface of the empire state building. You do this by dividing the surface area of the empire state building by the surface area of a piece of paper.
187 ft x 424 ft= 79,288 ft
187 ft x 1454 ft = 271,898 ft
271,898 ft x 4 = 1,087,592 ft
1,087,592 ft + 79,288 ft = 1,166,880
1,166,880 square feet ≈ 1,167,000 square feet
1,167,000 in Science Notation 1.167 x 10^6 square feet
11 inches x 8.5 inches = 93.5 square inches
1.167 x 10^6 square ft x 144 = 168048000 x 10^6 square inches
144 square inches = 1 square foot
1.68048x 10^14 square inches
____________________
93.5 square inches
1.68048x 10^14 square inches / 93.5 square inches = 1,797,304,812,834 pieces of printer paper
1,797,304,812,834 printer paper x .015 cents = 26,959,572,192.5 cents
26,959,572,192.5 cents / 100 = 269,595,721.92 $
It would cost 269,595,721.92 $ to cover the entire empire state building with printer paper.That enough money to buy 67 Lamborghini Venenos or spend 11 years in a 10 room and 7 bathroom hotel room at Hotel President Wilson in Geneva.
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