I was shopping for some toilet paper, I saw an advertisment for double the amount of toilet paper as a single roll. Assuming that the toilet paper is equally densely packed, and that the diameter of the core is the same at 1 unit, and the diameter of the original roll is 5 units, what is the diameter of the new roll?


 Jun 22, 2020



That means that instead of the (2.5)^2 π area, we have...




So, 2.5^2 = 6.25 


minus (0.5)^2 π = 0.25π for the area of the middle



12π+0.25π = 12.25π


sqrt(12.25) = 3.5


7 units diameter


Oops I made a mistake earlier, Corrected now

 Jun 22, 2020
edited by hugomimihu  Jun 22, 2020

The original roll has a diameter of 5 unts   --->   radius = 2.5 units.

It's total area is  pi·2.52  =  6.25pi units2.

However, not all of that is paper; there is a hollow core of diameter 1 unit   --->   radius = 0.5 units.

The area of the core is  pi·0.52  =  0.25pi units2.

Subtracting the area of the core from the total area gives  6.25pi units2 - 0.25pi units2  =  6.00pi units2.


To get twice the amount of paper:  2 x 6.00pi units2  =  12.00pi units2.

However, we can't forget the core, so we need  12.00pi units2 + 0.25pi units2  =  12.25pi units.


Finding the square root of 12.25, we get 3.5, so the roll needs a radius of 3.5 units,

which is a diameter of 7 units.

 Jun 22, 2020

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