A copper ball that has an air cavity immersed in kerosene, the outer volume is 0.1

A copper ball that has an air cavity immersed in kerosene, the outer volume is 0.1, find the volume of the air cavity if the ball floats by submerging 0.89 of its volume.

V = 0.1 m3.

Vp = 0.89 * V.

ρm = 8920 kg / m3.

ρк = 800 kg / m3.

g = 9.8 m / s2.

Vair -?

The force of gravity m * g, which acts on the copper ball, is balanced by the buoyancy force of Archimedes Farch: m * g = Farch.

m = ρm * Vm, where Vm is the volume of copper.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρк * g * Vт. Where ρк is the density of the liquid 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 liquid.

Farch = ρк * g * 0.89 * V.

ρm * Vm * g = ρk * g * 0.89 * V.

Vm = ρk * 0.89 * V / ρm.

Vm = 800 kg / m3 * 0.89 * 0.1 m3 / 8920 kg / m3 = 0.008 m3.

Vair = V – Vm.

Vair = 0.01 m3 – 0.008 m3 = 0.002 m3.

Answer: the volume of the air void is Vair = 0.002 m3.