Long fibers or stratified media show very long range correlations. This media can be simulated by models of Boolean random varieties. We study for these models the non standard scaling laws of the variance of the local volume fraction with the volume of domains K: on a large scale, a the variance of the local volume fraction decreases with power laws of the volume of K. The exponent γ is equal to 23 for Boolean fibers in 3D, and 1 3 for Boolean strata in 3D. When working in 2D, the scaling exponent of Boolean fibers is equal to 12 . These laws are expected to hold for the prediction of the effective properties of such random media from numerical simulations.