Isometric immersion of a compact Riemannian manifold into a Euclidean space

We show that an isometric immersion of an n −dimensional compact Riemannian manifold of non-negative Ricci curvature with scalar curvature always less than n ( n −1)λ −2 into a Euclidean space of dimension n + 1 can never be contained in a ball of radius λ.