floating object box n fluids

floating | buoyant | sinking - 1 fluid

$$\tag{1} \rho_2 \le \rho_1, \ \ \ \ \ \ \ \ \rho_2 = \rho_1, \ \ \ \ \ \ \ \ \rho_3 = \left( 1 + \frac{h_1}{h_3} \right) \rho_1 $$

floating & sinking - 2 fluids

$$\tag{2} h_2 \rho_2 + h_3 \rho_3 = \left( h_2 + h_3 \right) \rho_1 $$

floating & buoyant & sinking - 3 fluids

$$\tag{3} h_2 \rho_2 + h_3 \rho_3 + h_4 \rho_4 = \left( h_2 + h_3 + h_4 \right) \rho_1 $$