Geometrical Considerations in the Measurement of the Volume of an Approximate Sphere
1Institute for Basic Standards, National Bureau of Standards, Washington, D.C. 20234.
Abstract:
Expressions are derived for the volume of an approximate sphere in terms of measured breadth, the distance between parallel planes tangent to opposite sides. The difference in volume of a ball and a true sphere of the same average breadth is shown to be of second order, and much smaller than the random and systematic errors in the measurements of the dimension. Thus, a ball commercially available at moderate cost can be used for absolute density measurements of high accuracy. Similar expressions are given for the area of an approximate circle.
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