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

21.28 kg

Step-by-step 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=(m_i)/(v)\\\Rightarrow v=(m)/(\rho)\\\Rightarrow v=(8.7)/(7890)`

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

Mass of iron =
`m_i`

`\rho_g=(m_g)/(v)\\\Rightarrow m=\rho_g v\\\Rightarrow m_g=19300* (8.7)/(7890)\\\Rightarrow m_g=21.28\ kg`

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