Table 1.

Examples for roots or cohorts of flat round objects with the same average diameter (weighted by length/number) and the same length/sample size but different diameter distributions.

	Diameter	Length (root) or Number (flat)	Volume (root) or Surface area (flat)	Length (from volume)	Divergence (%)
E1	2	80	251.33	80
E2	1	10	7.85	10
	2	60	188.50	60
	3	10	70.69	10
Total	2	80	267.04	85	6.25
E3	1	20	15.71	20
	2	40	125.66	40
	3	20	141.37	20
Total	2	80	282.74	90	12.5
E4	1	40	31.42	40
	3	40	282.74	40
Total	2	80	314.16	100	25

The root volume or the surface area for flat objects are calculated per fraction of equal diameter and subsequently summed up. The length is then calculated for the different fractions again or from the correct volumes (Total). The divergence is the percentage of underestimation of volume (reference 251) or overestimation of length (reference 80) calculated following Equation 4. E1 represents constant diameter or results based on the average diameter. Bold values indicate total sample values.