Area component of structures within a larger area is proportional to the volume component of structures within the larger volume
The concept of morphometry is shown in these illustrations where a sectional plane is taken through a large cubical object containing smaller spheres within. The amount of surface area of the spheres exposed is proportional to the volume component that they occupy within the larger volume. The sectional area and, therefore, the volume component of the spheres in (a) is clearly greater than that in (b).
This principle is based on a study by a French Geologist, M. A. Delesse, who in 1847 showed that the volume density of different mineral substances in a rock could be determined from their densities revealed in exposed sections of the rock. In the latter 20th century this concept became utilized with biological materials that were sectioned for either light or transmission electron microscopy.
Illustration from: E. R. Weibel, 1963, Morphometry of the Human Lung, Springer, Berlin & Academic Press, N.Y.