The brass figurine weighs 42.2N in air and 22.6N in water. what is the volume of the air cavity inside the figurine?

The brass figurine weighs 42.2N in air and 22.6N in water. what is the volume of the air cavity inside the figurine? Density of brass 8500 kg / m³, density of water 1000 kg / m³

Rozd = 42.2 N.

Rvod = 22.6 N.

ρl = 8500 kg / m3.

ρw = 1000 kg / m3.

g = 9.8 m / s2.

Vair -?

We express the weight of the body in the air Rvozd by the formula: Rvozd = m * g.

m = ρl * Vl, where Vl is the volume of brass.

Rozd = ρl * Vl * g.

Vl = Rozd / ρl * g.

Vl = 42.2 N / 8500 kg / m * 9.8 m / s2 = 0.0005 m3.

Body weight in water Rvod is determined by the formula: Rvod = m * g – Farch.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρw * g * Vt. Where ρw is the density of the fluid in which the body is immersed, g is the acceleration of gravity, Vt is the volume of the immersed part of the body in the fluid.

Rvod = Rvozd – ρw * g * Vt.

Vt = (Rvozd – Rvod) / ρw * g.

Vt = (42.2 N – 22.6 N) / 1000 kg / m3 * 9.8 m / s2 = 0.002 m3.

Vair = Vt – Vl.

Vair = 0.002 m3 – 0.0005 m3 = 0.0015 m3.

Answer: the volume of the air cavity inside the figurine is Vair = 0.0015 m3.