$F_c=F_{wyp}$

$F_c=mg$

$F_{wyp}={\rho }_w{V}_{zan}g$

$m\cancel{g}={\rho }_w{V}_{zan}\cancel{g}$

${\rho }_{l}V={\rho }_w{V}_{zan}$

${\rho }_{l}V={\rho }_w\left(V-V_w\right)$

${\rho }_{l}V={\rho }_{w}V-{\rho }_w{V}_w|+{\rho }_w{V}_w$

${\rho }_{l}V+{\rho }_w{V}_w={\rho }_{w}V|-{\rho }_{l}V$

${\rho }_w{V}_w={\rho }_{w}V-{\rho }_{l}V$

${\rho }_w{V}_w=\left({\rho }_w-{\rho }_l\right)V|:{\rho }_w$

$V_w=\frac{{\rho }_w-{\rho }_l}{{\rho }_w}V$

$V_w=\frac{1040\frac{\mathrm{kg}}{{\mathrm{m}}^3}-900\frac{\mathrm{kg}}{{\mathrm{m}}^3}}{1040\frac{\mathrm{kg}}{{\mathrm{m}}^3}}V$

$V_w\approx 0,135V\approx 13,5\%V$