Question

An automobile company displays a die-cast model of its first car, made from 8.70 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?

Answer 1

Answer:

21.28 kg

Explanation:

Density of iron = 7890 kg/m³ =$\rho_i$

Mass of iron = 8.7 kg=$m_i$

Volume of gold = Volume of iron = v

Density = Mass / Volume

$\rho_i=\frac{m_i}{v}\\\Rightarrow v=\frac{m}{\rho}\\\Rightarrow v=\frac{8.7}{7890}$

Density of gold = 19300 kg/m³=$\rho_g$

Mass of iron =$m_i$

$\rho_g=\frac{m_g}{v}\\\Rightarrow m=\rho_g v\\\Rightarrow m_g=19300\times \frac{8.7}{7890}\\\Rightarrow m_g=21.28\ kg$

Mass of gold needed to make the new model is 21.28 kg