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According to Zimmels (1983), the sizes of particles used
Chapter 4, Problem 57E(choose chapter or problem)
Problem 57E
According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. Thus, it is important to study both the mean and the variance of particle sizes. Suppose that spherical particles have diameters that are uniformly distributed between .01 and .05 centimeters. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is (4/3)πr 3.)
Questions & Answers
QUESTION:
Problem 57E
According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. Thus, it is important to study both the mean and the variance of particle sizes. Suppose that spherical particles have diameters that are uniformly distributed between .01 and .05 centimeters. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is (4/3)πr 3.)
ANSWER:
Solution:
Step 1 of 3:
Given that the volume of sphere is .
Where, r is the radius and d is the diameter.
Assume D is diameter such that, D is the uniform distribution on the interval (0.01, 0.05).
= 25