2. An automobile company displays a die-cast model of its first car, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in solid gold from the original dies. What mass of gold is needed to make the new model?
Given:
Density of iron: `ρ_i = 7.86 times 10^3 kg//m^3`
Density of gold: `ρ_g = 1.93 times 10^4 kg//m^3`
The volume of both models are same, `ρ=m/V`
23.0 kg
From `ρ=m/V` we get `V = m/ρ`
Since volume of iron model and gold model are same:
`V_i = V_g`
`m_i/ρ_i =m_g/ρ_g`
`m_g = m_i(ρ_g/ρ_i)`
`=(9.35 kg)((1.93 times 10^4 kg//m^3)/(7.86 times 10^3 kg//m^3))`
`= 23.0 kg`
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