Diameter estimate of the manifolds with positive Ricci curvature and reverse volume pinching

We show that for any integer n⩾3, there exists a positive number η(n) depending only on n such that if Mn is a complete simply connected n-dimensional Riemannian manifold whose sectional curvature, Ricci curvature and volume satisfy the conditions KM⩽1, Ric(M)⩾(n+2)/4 and 0