Amajor 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

22.10 kg

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:

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:

so we can rewrite the first equation as

where we have

is the mass of the model in iron

is the density of iron

is the mass of gold needed

is the density of gold

Solving for , we find

the independent variable, or the one that is intentionally manipulated is the speed.