In this paper we study a class of oriented hypersurfaces in Euclidean space, namely, the hypersurfaces of the spherical type, this class of hypersurfaces includes the surfaces of the spherical type (Laguerre minimal surfaces) studied in [8]. We show that for n = 2, the classes of surfaces of the spherical type and the Weingarten surfaces of the spherical type coincide, more for larger dimensions this is not true and we give explicit examples. We also introduced a class of hypersurfaces associated to a biharmonic map and we show that the hypersurfaces of the spherical type are associated to a biharmonic map. Moreover, we classify the hypersurfaces of the spherical type of rotation.