Thread: Need help with geometry problem

This is probably pretty simple for a lot of you, quick help would be much appreciated.



"A woman was shopping for toilet tissue. She saw a new brand selling packs of four rolls with 240 sheets per roll. She knew the tissues were 14 cm long and estimated the diameter of the tolls to be 11 cm, wound around cardboard cylinders of diameter 4cm. At first she was concerned that the tissues were would onto the roll in a spiral with increasing radius, but she eventually found her way around this problem and found the tissues thickness.
How thick was the tissue?
About how many turns of tissue paper are on each roll?"

Thank you!

you want to find the surface area of the side of the roll (the amount of area that one side of a stack of 240 tissues would occupy):

A = pi*r1^2 - pi*r2^2

If you divide that area by 240, you get the area that one side of one tissue would occupy. Since we know the length of one tissue, the only unknown we have is thickness.

A = (length of the tissue)(thickness of the tissue)

plug in the area you found in the previous step and the length of the tissue and solve for thickness.


For the amount of turns, I think this is how you do it:

You know the length of one tissue and also the number of tissues on the roll so you can calculate the total length of tissue of the roll.
Next, you want to calculate the average circumference the tissue will need to traverse to complete one roll.

C = 2(avgradius)*pi = 2((2+5.5) /2)*pi

so then just divide the total length of tissue by the average circumference and you get the number of turns on a roll.

Thanks a lot!

For the amount of turns, I think this is how you do it:

You know the length of one tissue and also the number of tissues on the roll so you can calculate the total length of tissue of the roll.
Next, you want to calculate the average circumference the tissue will need to traverse to complete one roll.

C = 2(avgradius)*pi = 2((2+5.5) /2)*pi

so then just divide the total length of tissue by the average circumference and you get the number of turns on a roll.

Not sure if that's right. The formula for the length of a spiral is a pretty complicated thing with arcsinhs and stuff, I don't think you can just calculate the 'mean' circumference...

I just look at it like this: you've got the width of the tissue, and you've got the width of the roll. Every time the tissue is wrapped around one time it adds an extra width, so nT = R, where T is the tissue width, R the roll width, and n the number of turns, so to solve just divide R by T.

Originally Posted by Xei

Not sure if that's right. The formula for the length of a spiral is a pretty complicated thing with arcsinhs and stuff, I don't think you can just calculate the 'mean' circumference...

I just look at it like this: you've got the width of the tissue, and you've got the width of the roll. Every time the tissue is wrapped around one time it adds an extra width, so nT = R, where T is the tissue width, R the roll width, and n the number of turns, so to solve just divide R by T.

Yea that way works, and probably more accurate. My way was just the first method that came to mind. I just figured we could approximate the roll to just be a series of concentric circles, but I worked it out both ways and you get about the same answer.