SOLUTION: A tight roll of paper as delivered to the printer is 60cm in diameter and the paper is wound onto a wooden cylinder 8cm in diameter. The paper is 0.005cm thick. What length of pape

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Question 1205007: A tight roll of paper as delivered to the printer is 60cm in diameter and the paper is wound onto a wooden cylinder 8cm in diameter. The paper is 0.005cm thick. What length of paper is there in the roll in km?
(Hint: Compare the area of the edge of the paper when rolled with that of the paper when unrolled)
Answer by ikleyn(52830) About Me  (Show Source):
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A tight roll of paper as delivered to the printer is 60cm in diameter and the paper
is wound onto a wooden cylinder 8cm in diameter. The paper is 0.005 cm thick.
What length of paper is there in the roll in km?
(Hint: Compare the area of the edge of the paper when rolled with that of the paper when unrolled)
~~~~~~~~~~~~~~~~~~~~~~~~ 

The given parameters are:

    Inner diameter d%5B1%5D =  8 cm

    Outer diameter d%5B2%5D = 60 cm 


The area between the two circles is

    Area = %28pi%2Ad%5B2%5D%5E2%29%2F4 - %28pi%2Ad%5B1%5D%5E2%29%2F4 = 3.14159265%2A%28%2860%2F2%29%5E2-%288%2F2%29%5E2%29 = 2777.167903 cm^2.


The length of the paper is then calculated as:

    Length = Area%2F0.005 centimeters.


This gives

   Length = 2777.167903%2F0.005 = 555433.5806 cm,  or  5554.34 meters.  (rounded).  


ANSWER.  The length of the paper in the roll is 5554.34 meters or 5.55434 kilometer (rounded).

Solved.