Answer:
3.666 × 10³ kg/m³
Step-by-step explanation:
Let's assume the volume of metal Y in the alloy is V cubic meters. Since the volume of metal X is twice that of Y, the volume of metal X would be 2V cubic meters.
The density of a substance is given by the formula:
Density = Mass / Volume
Let's assume the mass of metal X is Mx and the mass of metal Y is My.
For metal X:
Density of X = Mx / (2V) -- Equation 1
For metal Y:
Density of Y = My / V -- Equation 2
Given that the density of metal X is 3 × 10³ kg/m³ and the density of metal Y is 5 × 10³ kg/m³, we can rewrite Equations 1 and 2 as:
3 × 10³ = Mx / (2V) -- Equation 1
5 × 10³ = My / V -- Equation 2
To find the density of the alloy, we need to find the total mass of the alloy (M) and the total volume of the alloy (Vt). The total mass of the alloy is the sum of the masses of metal X and metal Y, and the total volume of the alloy is the sum of the volumes of metal X and metal Y.
M = Mx + My
Vt = 2V + V
We can rearrange Equation 1 to find Mx in terms of V:
Mx = 3 × 10³ * (2V) = 6 × 10³V
Substituting the values in the equation for M:
M = 6 × 10³V + My
We can substitute the value of Mx in Equation 2:
5 × 10³ = My / V
Rearranging Equation 2 to find My in terms of V:
My = 5 × 10³V
Substituting the values of Mx and My in the equation for M:
M = 6 × 10³V + 5 × 10³V
M = 11 × 10³V
The density of the alloy (Da) is given by the formula:
Da = M / Vt
Substituting the values of M and Vt:
Da = (11 × 10³V) / (2V + V)
Da = (11 × 10³V) / (3V)
Da = 11 × 10³ / 3
Simplifying further:
Da = 3.666 × 10³ kg/m³
Therefore, the density of the alloy is approximately 3.666 × 10³ kg/m³.