Question

A major motor company displays a die-cast model of its first automobile, made from 9.00kg of iron. To celebrate its hundredth year in business, a worker will recast the model in gold from the original dies. What mass of gold is needed to make the new model? The density of iron is 7.86 ✕ 10^3 kg/m3, and that of gold is 19.30 ✕ 10^3 kg/m3

Answer 1

22.10 kg

Step-by-step explanation:

The worker wants to recast the model from iron to gold, so the volume of the model made of iron and made of gold will be the same:

`V_i = V_g`

the volume of each model can be rewritten as the ratio between the mass of the model, m, and the density of the material, d:

`V=(m)/(d)`

so we can rewrite the first equation as

`(m_i)/(d_i)=(m_g)/(d_g)`

where we have

`m_i = 9.00 kg` is the mass of the model in iron

`d_i = 7.86\cdot 10^3 kg/m^3` is the density of iron

`m_g` is the mass of gold needed

`d_g = 19.30\cdot 10^3 kg/m^3` is the density of gold

Solving for
`m_g`, we find

`m_g = d_g (m_i)/(d_i)=(19.30\cdot 10^3 kg/m^3) (9.00 kg)/(7.86\cdot 10^3 kg/m^3)=22.10 kg`