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Errors in Measuring Volume of Small Balls in Large Container

Consider an experimental procedure to measure the average volume of M&M Peanut candies. One hundred piece of the candy are poured into a graduated cylinder with a 30 diameter. The cylinder is then filled with 1 mm diameter beads and shaken so that the beads and candies pack as tightly as possible. Finally, the candies are removed and the change in volume noted.
Compute the change in estimated volume if 0.1 mm dia beads were used in place of the 1 mm dia beads. Can you define a relationship that estimates the change in estimated volume of the candies based on the diameter of the beads used in the measurement?

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The source of error in this method of measuring volume is in the immediate vicinity of the surface of the candies, where the beads are, in general, imperfectly packed, and so more volume remains unoccupied than in the case of beads only. This volume of packing defects can be estimated as
Vd ~ ...

Solution Summary

The solution discusses the errors in measuring volume of small balls in a large container.