Surface area to volume ratio can be found easily for several simple shapes, like for example a cube or a sphere.
For
a cube, the equation for surface area is S=6*L*L, where L is the length
of a side. Similarly, the volume of a cube is V =L*L*L. So for a cube,
the ratio of surface area to volume is given by the ratio of these
equations: S/V = 6/L.
For a sphere, surface area is S= 4*Pi*R*R,
where R is the radius of the sphere and Pi is 3.1415... The volume of a
sphere is V= 4*Pi*R*R*R/3. So for a sphere, the ratio of surface area
to volume is given by: S/V = 3/R.
For other shapes you may be
able to look up the equations for surface area and for volume, or you
may be able to use surface integrals and volume integrals to calculate
them yourself (if you've taken calculus, that is.)
One
interesting thing that you should notice is that the surface area to
volume ratio is inversely proportional to the size of an object. For
example, we found that for a sphere S/V is 3/R. Since R tells us the
"size" we see that S/V is inversely proportional to this (in other
words, as R gets small the S/V ratio gets big). This trend is true for
any shape, and is the reason why icing sugar dissolves faster in water
than regular sugar, why water evaporates faster if you spray it as a
fine mist than if you leave it in a bucket, and why dusty grain
elevators sometimes explode if someone lights a match inside (see if
you can figure these examples out).
-Kim- (and Tamara & Mats)
(published on 10/22/2007)
