We prove that the cones, of dimension no less than \({\textbf{8}}\) , over minimal products (Tang and Zhang in J. Differential Geom. 115(2):367-393, 2020) among all irreducible symmetric R-spaces of classical type are area-minimizing based on Lawlor’s Curvature Criterion (Lawlor in Mem. Am. Math. Soc. 91(446):1-111, 1991). Moreover, those minimal product cones are natural generalizations for classical minimal cones over products of spheres, and for the critical situations—the cones of dimension \({\textbf{7}}\) , we give some \({\textbf{7}}\) -dimensional area-minimizing cones by carefully computing the minimum of Jacobian functions det \((I-tA_{v})\) for their link submanifolds in unit spheres. Based on Curvature Criterion, our results are sharp, and it develops related researches in Jiao et al. (Calc. Var. Partial Differential Equ. 61(6):205, 2022), Kanno (Indiana Univ. Math. J. 51(1):89-125, 2002), Tang and Zhang (J. Differential Geom. 115(2):367-393, 2020).
