Question

3 points

15. Metal A has a density of 2.4g/cm3 and Metal B has a density of 1.8
g/cm3. Their masses are combined in the ratio 2:3 to make metal C which
has a mass of 60 grams. Find the density of the metal C*

Answer 1

The density of the metal C is 2 g/cm³

Explanation:

The parameters of the two metals are;

The density of the Metal A = 2.4 g/cm³

The density of the Metal B = 1.8 g/cm³

The ratio in which their masses are combined to make the metal C= 2:3

The mass of the metal C, m = 60 grams

Let, 'x', represent the mass of the metal A in the 60 grams of the metal C and let 'y' represent the mass of the metal B in the 60 grams of the metal C

Let the ratio of the metals A and B in the metal C = x:y = 2:3

Therefore;

The mass of the metal A in the metal C, x = (2/(3 + 2)) × 60 g = 24 g

The volume of the metal A in the metal C, V₁ = (24 g)/(2.4 g/cm³) = 10 cm³

The mass of the metal B in the metal C, y = (3/(3 + 2)) × 60 g = 36 g

The volume of the metal B in the metal C, V₂ = (36 g)/(1.8 g/cm³) = 20 cm³

The volume of the metal C, V = V₁ + V₂ = 10 cm³ + 20 cm³ = 30 cm³

The density of the metal C = ρ = m/V

ρ = (60 g)/(30 cm³) = 2 g/cm³

The density of the metal C, ρ = 2 g/cm³