  In this article, we present an example of an inhomogeneous cosmological
model, which is inspired by the linear perturbation theory. The metric of this
model can be described as the Einstein-de Sitter background with a periodically
distributed dust overdensities. The model construction enables application of
the Green-Wald averaging scheme and the Buchert averaging technique
simultaneously. We compare the angular diameter distance function of the
considered model to the angular diameter distances corresponding to the average
space-times given by the Green-Wald and the Buchert frameworks respectively.
