A hollow zinc ball, the outer volume of which is 200cm ^ 3, floats in water so that half

A hollow zinc ball, the outer volume of which is 200cm ^ 3, floats in water so that half of it is submerged in water. calculate the volume of the ball density of zinc 7100 kg / m ^ 3

V = 200 cm3 = 0.0002 m3.

ρc = 7100 kg / m3.

ρw = 1000 kg / m3.

Vv = V / 2.

Vп -?

The volume of the cavity of the ball Vp is expressed by the formula: Vp = V – Vc, where Vc is the volume of zinc.

The condition for finding the ball in the water: m * g = Farch.

Vts * ρts * g = Vw * ρw * g.

Vts * ρts * g = V * ρw * g / 2.

Vc = V * ρw * g / 2 * ρc * g = V * ρw / 2 * ρc.

Vc = 0.0002 m3 * 1000 kg / m3 / 2 * 7100 kg / m3 = 0.000014 m3.

Vp = 0.0002 m3 – 0.000014 m3 = 0.000186 m3 = 186 cm3.

Answer: the volume of the cavity of the zinc ball, which is half submerged in water, is Vp = 186 cm3.