Abstract: To study the relationship among geometric quantities (the curvature, the diameter and the volume) ofRiemannianmonifolds is a significant project in geometry. As to the questionwhetherthe volume V(M)has a positive lower bound for them-dimensional Riemannian monifoldsMsatisfying that the curvatureK(M)≥1, the diameterd(M)≥γπ,0<γ<1,this paper gives a negative answer through constructing an ellipsoidal model and directly calculating the geometric quantities. Thus the problem is thoroughly solved from one aspect