Consider a non-degenerate convex body K in a Euclidean (n + 1)-dimensional space of points (x, z) = (x1,…, xn, z) where n ≧2. Denote by μ the maximum length of segments in K which are parallel to the z-axis, and let Aj, signify the area (two dimensional volume) of the orthogonal projection of K onto the linear subspace spanned by the z- and xj,-axes. We shall prove that the volume V(K) of K satisfies After this, some applications of (1) are discussed.