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### Calculating the Diameter of a Carpet Roll

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Date: 9/24/95 at 12:36:46
From: Anonymous
Subject: Calculating the diameter of a roll

How do you calculate the diameter of a carpet roll
when you have the length and the thickness?

Thanks in anticipation.

Filip
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Date: 9/24/95 at 18:36:18
From: Doctor Andrew
Subject: Re: Calculating the diameter of a roll

Hi!  Great question.  For a darn good approximation you could
find the cross-sectional area (the area of the circular end of
the roll) needed for the roll, assume that the roll is a
perfect cylinder, and then calculate the diameter required for
that cross-sectional area.  If a carpet has length l and
thickness t, the cross-sectional area of the roll is the same
as the cross-sectional area of the edge of the carpet when it
is lying on the floor, which is the very long rectangle with
length l and thickness t.  See if you can take it from here to
find the diameter.

Neither of us has ever seen a carpet roll shaped perfectly
cylindrically since it is a spiral with an edge that usually
sticks out off the rest of the roll.  I imagine that trying to
describe the shape of the spiral could be pretty tough.  You
could probably come up with a number of approximations, the
most accurate of which would take into account how the spiral
begins and what kind of space would be left in the center of
the roll due to physical limitations on how the carpet can
bend.  You might notice that the approximation in the above
paragraph becomes less and less accurate as the ratio of l to t
(the fraction l/t) becomes smaller and smaller.  If you think
more about it, you'll realize that when a carpet bends it is
already changing its shape (stretching on the outside,
compressing on the inside) in a way that makes describing it
exactly with mathematics very difficult.

back.

-Doctor Andrew, The Geometry Forum
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Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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