To obtain brass, pieces of copper with a mass of 178 kg and zinc with a mass of 355 kg were fused.

To obtain brass, pieces of copper with a mass of 178 kg and zinc with a mass of 355 kg were fused. Determine the density of brass, considering the volume of the alloy equal to the sum of the volumes of its constituent parts.

Given:

m1 = 178 kilograms is the mass of copper;

ro1 = 8900 kg / m ^ 3 – copper density;

m2 = 355 kilograms – the mass of zinc;

ro2 = 7130 kg / m ^ 3 is the density of zinc.

It is required to find the density of the alloy (brass) ro3 (kg / m ^ 3).

Find the volume of copper:

V1 = m1 / ro1 = 178/8900 = 0.02 m ^ 3.

V2 = m2 / ro2 = 355/7130 = 0.05 m ^ 3 – the volume of zinc.

By the condition of the problem, V3 = V1 + V2, then:

ro3 = m3 / V3 = (m1 + m2) / (V1 + V2) = (355 + 178) / (0.02 + 0.05) = 533 / 0.07 = 7614 kg / m ^ 3.

Answer: the density of brass is 7614 kg / m ^ 3.