In this paper, we study the complete bounded λ-hypersurfaces in
weighted volume-preserving mean curvature flow. Firstly, we investigate the
volume comparison theorem of complete bounded λ-hypersurfaces with
∣A∣≤α and get some applications of the volume comparison theorem.
Secondly, we consider the relation among λ, extrinsic radius k,
intrinsic diameter d, and dimension n of the complete
λ-hypersurface, and we obtain some estimates for the intrinsic diameter
and the extrinsic radius. At last, we get some topological properties of the
bounded λ-hypersurface with some natural and general restrictions