Question

Density of copper is 8.96 g/cm3and density of zinc is 7.14 g/cm3. Brass is an alloy made of copper and zinc. You are given a sample of brass with the density of 8.32 g/cm3. The price of zinc is $1.80/kg and price of copper is $6.13/kg. Determine the material cost for making one ton of the brass sample that you ha

Answer 1

The material cost for making one ton of the brass sample that I have is $8149.04.

Step-by-step explanation:

Density of copper = 8.96 g/cm^3 = 8.96×10^-3 kg/cm^3

Price of copper = $6.13/kg

Price of copper per volume = 8.96×10^-3 kg/cm^3 × $6.13/kg = $0.0549/cm^3

Density of zinc = 7.14 g/cm^3 = 7.14×10^-3 kg/cm^3

Price of zinc = $1.8/kg

Price of zinc per volume = 7.14×10^-3 kg/cm^3 × $1.8/kg = $0.0129/cm^3

Price of brass per volume = 0.0549 + 0.0129 = $0.0678/cm^3

Density of brass I have is 8.32 g/cm^3 = 8.32 g/cm^3 × 1 kg/1000 g × 1 ton/1000 kg = 8.32×10^-6 ton/cm^3

Price = $0.0678/cm^3 ÷ 8.32×10^-6 ton/cm^3 = $8149.04/ton

Answer 2

The Price of making 1 Ton of Brass is = $4180.4

Step-by-step explanation:

Generally density of an alloy is mathematically represented as

`Z = \sum A *\rho`

Where Z is the Average density of an alloy

A is the fraction of metal

`\rho` is the density of metal

From the question we are told that brass is an alloy made of copper and zinc

Let assume that the percentage of copper in Brass is y%

The the percentage of the zinc would be (100 - y )%

Substituting this into the formula

`8.32 g/cm^3 =(y)/(100) * 8.96 + ((100 -x))/(100) * 7.14`

=>
`832 = 8.96y + 714 - 7.14y`

=>
`8.96y - 7.14y = 832-714`

=>
`1.82y = 118`

=>
`y = (118)/(1.82) = 64.84`%

This implies that the percentage of copper in Brass is 64.84%

This mean that the percentage of zinc in Brass is (100- 64.84) = 35.16%

Generally One Ton of Brass = 907.185Kg

So amount of copper in this is

`= (64.84)/(100) * 907.185 = 588.29 Kg`

And the price would be
`= 588.29 * 6.13 =` $3606

And the amount of zinc is
`= (35.16)/(100) * 907.185 =318.97Kg`

And the price would be
`= 318.97 * 1.80=` $574.146

The Price of making 1 Ton of Brass is = 3606 + 574.146 = $4180.4