6.24 According to Y. Zimmels (AIChE journal, 29(4), 1983, pp. 669–676), the sizes of particles used in sedimentation experiments often have uniform distributions. It is important to study both the mean and variance of particle sizes, since in sedimentation with mixtures of various-size particles the larger particles hinder the movements of the smaller ones. Suppose spherical particles have diameters uniformly distributed between 0.01 and 0.05 centimeter. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is .)