  In this note we show the following result using the integral-geometric
formula of R. Howard: Consider the totally geodesic $\mathbb{R}P^{2m}$ in
$\mathbb{C}P^n$. Then it minimizes volume among the isotropic submanifolds in
the same $\mathbb{Z}/2$ homology class in $\mathbb{C}P^n$ (but not among all
submanifolds in this $\mathbb{Z}/2$ homology class). Also the totally geodesic
$\mathbb{R}P^{2m-1}$ minimizes volume in its Hamiltonian deformation class in
$\mathbb{C}P^n$. As a corollary we'll give estimates for volumes of Lagrangian
submanifolds in complete intersections in $\mathbb{C}P^n$.
