Consider three spherical particles with diameters of 1 mm, 2 mm, and 3 mm. Determine: a. the arithmetic average length diameter ( x1 0, ), b. the arithmetic average surface area diameter ( x2 0, ), c. the arithmetic average volume diameter ( x3 0, ), d. the Sauter mean diameter (the weighted average surface area diameter, x32 ), and e. the de Brouckere mean diameter (the weighted average volume diameter, x43 ).