# Talk:Surface-area-to-volume ratio

WikiProject Molecular and Cellular Biology (Rated C-class, Low-importance)
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The lead states "For a given shape, SA:V decreases linearly with increasing size". This is only true given some assumptions on the geometry. Fractals are an example where this statement is not as trivial, see fractal dimension. --Berland (talk) 19:05, 3 June 2009 (UTC)

The associated page contains a mistake, or at least a misleading presentation. For instance, in the table regarding SA:V, for the cube, the variable "a" denotes a diameter. Yet, in the case of the sphere, it denotes a radius. The SA:V of cube and sphere are identical, 3/r, where r is the radius or, in the case of the cube, the half-side, or the length of the perpendicular projection of a normal from a side going through the cube's center.

The comparison of cube to sphere or sphere to any other shape should use an equivalent radius. This radius can be derived either by equating the areas of the two solids, obtaining the radius, and then calculating the surface-area-to-volume ratio using it, or by equating the volumes of the two solids, obtaining the radius, and then calculating. If, for instance, the area of a sphere is equated to the area of a cube, the equivalent radius is sqrt(3/(2*pi))*a, using the nomenclature on the page. The corresponding SA:V ratio is sqrt(6*pi)/a. If the volume of a sphere is equated to the volume of a cube, the equivalent radius is a times cube root of 3/(4*pi), and the corresponding SA:V is a divided into the cube root of 4/(3*pi).

--Jan Galkowski disneylogic (talk) original 20:45, 17 September 2010 (UTC), revised 72.246.0.10 (talk) 15:56, 18 September 2010 (UTC)

## Citations?

It could use some. This is a handy concept article, but it cites, like, nothing. 24.29.9.104 (talk) 22:20, 8 August 2013 (UTC)Ubiquitousnewt