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MEASUREMENT
Lesson 5 - Page 2

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It is interesting to compare the overall surface area of an object with its volume.  The volume increases disproportional to the surface area.  The increase in volume is greater than the corresponding increase in surface area.  Conversely, as an object becomes smaller, its surface area increases when compared to its volume or weight.  In living organisms, small cells have a large surface area in comparison to their size, and this is crucial to their existence.  As cells increase in size the surface area decreases.   This not only relates to cells but applies to crystals and all other matter.  The increase in volume is always greater than the increase in surface area. This is true for cubes, spheres, or any other object whose size is increased without changing its shape.

Letís see if we can develop a surface area (SA) to volume (V) (SA/V) ratio and compare them.  We will use four different cubes that you will make and then measure the edges and calculate surface area and volume.  We will plot the relationship of volume to surface area on a graph then compare with another graph.   The surface area of a cube can be determined by length x width x 6 sides  or  SA (cube) = 6lw, but since length = width in a cube, the formula is 6s2.  The volume is just multiplying length x width x height or volume (cube) = lwh.  Since a cube has all equal sides the formula for volume (v) = s3.

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