SOLUTION: Which has greater volume . A piece of paper rolled into a cylinder Lengthwise Or .A piece of paper rolled into a cylinder widthwise

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Question 1151128: Which has greater volume
. A piece of paper rolled into a cylinder Lengthwise Or
.A piece of paper rolled into a cylinder widthwise
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
If length of the paper is y, and width of the paper is x,
,

and if the paper is rolled so that the circumference is y, then volume is

and if paper is rolled so that circumference is x, then volume is .
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
Rolling the cylinder lengthwise means that the circumference of the cylinder becomes the magnitude of the , and the height is the magnitude of the

so, if the circumference of the cylinder is

Then the volume is:






if the circumference of the cylinder is


Then the volume is:






Dividing the width folding by the length folding:


Thus the ratio of the two volumes is the ratio of the length to the width (interesting.) So the width folding has greater volume.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            Start from learning on  "what a paper roll is".

            Type these words into the  GOOGLE  search engine and look into the  images  it will produce for you in response.


Solution 

Total mass is the same;


the density of the paper is the same in both cases


    ========> h e n c e =========>


the volume  MUST  be  THE  SAME  in both cases.

----------------

Had they be different,  then the  "PERPETUUM  MOBILE"  would be possible to construct  (!)  (!)  (!)


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