A solid hemisphere of radius \(R\) has its flat circular base centered at the origin in the \(xy\)-plane, with its curved surface extending along the positive \(z\)-axis from \(z = 0\) to \(z = R\). The volume mass density of the hemisphere varies with height \(z\) above the base according to \(\rho(z) = \rho_0 \left(\dfrac{z}{R}\right)\), where \(\rho_0\) is a positive constant. Which of the following expressions represents the \(z\)-coordinate of the hemisphere's center of mass, \(z_{\text{cm}}\)?