Isoperimetric QuotientDate: 03/11/2002 at 09:20:40 From: Andreas Mantius Subject: Surface Area to volume ratio I have a question about a ratio equation of surface area to volume. I can't remember if its SA/V or V/SA. Andreas Date: 03/11/2002 at 12:38:34 From: Doctor Peterson Subject: Re: Surface Area to volume ratio Hi, Andreas. The ratio of surface area to volume is by definition A/V; but that is not a meaningful quantity, because it depends on the units you use. A measure of "efficiency" that you might have heard of for plane figures is the isoperimetric quotient: Isoperimetric Quotient - MathWorld, Eric Weisstein http://mathworld.wolfram.com/IsoperimetricQuotient.html Area and Perimeter: Isoperimetric Quotient - Dr. Math archives http://mathforum.org/dr.math/problems/ace.12.05.01.html Q = 4 pi A / P^2 which for a circle is Q = 4 pi (pi r^2) / (2 pi r)^2 = 1 The equivalent for a solid figure, which I haven't heard of, would be an "isoareal quotient" Q = 36 pi V^2 / S^3 which I chose so that for a sphere, Q = (36 pi) (4/3 pi r^3)^2 / (4 pi r^2)^3 = 1 At any rate, since area is measured in square units and volume in cubic units, the ratio of the square of the volume to the cube of the surface area is what you need to eliminate dependence on units and consider only the shape itself. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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