A rectangular piece of paper can be rolled into a tube in two different ways. (Edges should not overlap.)

When it is rolled up the long way the volume enclosed is 2500/π cm³.
When is is rolled up the short way the volume enclosed is 3125/π cm³.

Find the area of the piece of paper.

let the long way have volume a/ð and the short way b/ð

then using similar method as in my previous solution we have

xy^2=4a

x^2y=4b

4a/(4b)=a/b=(xy^2)/(x^2y)=y/x thus

y=ax/b

thus

ax^3/b=4b

x^3=4b^2/a

x=(4b^2/a)^(1/3) and thus

y=(a/b)*(4b^2/a)^(1/3)=(4a^2/b)^(1/3)

thus the area is

xy=(16ab)^(1/3)

Posted by Daniel on 2009-06-16 02:05:15