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.
lets say that the paper has dimensions x,y with x≥y then we have
that the radius for the long way is y/(2π) and thus the volume is
xy^2/(4π)
and thus we have
xy^2=10000
and for the short way we have the radius as x/(2π) and thus the volume is
x^2y/(4π)
and thus we have
x^2y=12500
y=12500/x^2
and substituting in above we have
156250000/x^3=10000
x^3=15625
x=25
and thus
y=12500/625=20
and thus the area is
xy=25*20=500
|
|
Posted by Daniel
on 2009-06-15 19:05:41 |
solution
