Calculating the Diameter of a Carpet Roll
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
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. Thanks for your question. If you need more help, please write back. -Doctor Andrew, The Geometry Forum
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