An iron bar floats in mercury; how much of its volume is immersed in mercury?

An iron bar floats in mercury; how much of its volume is immersed in mercury? Density of iron 7800 kg / m3, density of mercury 13600 kg / m3

ρzh = 7800 kg / m ^ 3.
ρрт = 13600 kg / m ^ 3.
Vп / V -?
Two forces act on an iron bar that floats: the force of gravity Ft directed vertically downward, and the buoyancy force of Archimedes Farch directed vertically upward.
Ft = Farch.
The force of gravity is determined by the formula: Ft = m * g, where m is the mass of the body, g is the acceleration of gravity.
m = ρl * V.
Fт = ρж * V * g.
The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρрт * g * Vп, where ρрт is the density of mercury, Vп is the volume of a body immersed in mercury.
ρl * V * g = ρрт * g * Vп.
Vp / V = ​​ρl / ρrt.
Vp / V = ​​7800 kg / m ^ 3/13600 kg / m ^ 3 = 0.57.
Answer: the body is immersed in mercury by 0.57 parts of the total volume of the body Vp / V = ​​0.57.