We propose a content-based method for retrieving the 3D CAD assemblies which contain or are contained in the assembly given as a query from a database. The retrieval is based on ranking assemblies in the database according to their content rates which are different criteria from the similarities of shapes. The content rate is computed by comparing the projections of components constituting an assembly in the database with those of components constituting the query. We use the 3D Radon transform to obtain the projections. In existing methods for retrieving CAD models, projections of each model onto 2D planes, which are a set of two-dimensional data, are often used to compute the similarity between them. The proposed method simplifies the process of comparing the projections of components because the projections using the 3D Radon transform are a set of one-dimensional data. The method has the unique feature of identifying the component layouts, which reflect the technical know-how and information of the product designers. The components which have the same shapes but different properties such as material names are also distinguished based on their layouts without depending on the labels assigned to the properties. Other than our previous method, no existing methods possess such features. We show that the proposed method has better performance in the retrieval precision and processing time than the previous method.