Answer:
21.28 kg
Explanation:
Density of iron = 7890 kg/m³ =[tex]\rho_i[/tex]
Mass of iron = 8.7 kg=[tex]m_i[/tex]
Volume of gold = Volume of iron = v
Density = Mass / Volume
[tex]\rho_i=\frac{m_i}{v}\\\Rightarrow v=\frac{m}{\rho}\\\Rightarrow v=\frac{8.7}{7890}[/tex]
Density of gold = 19300 kg/m³=[tex]\rho_g[/tex]
Mass of iron =[tex]m_i[/tex]
[tex]\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[/tex]
Mass of gold needed to make the new model is 21.28 kg
