3g of metal A of density 2.7g/cm3 is mixed with 2.4dm3 of metal B of density 4.8g/cm3.Determine the density of the mixture

Question

Mixtures density,mass and volume

Answer 1

Density=mass/volume, so volume=mass/density.

Volume of A=3/2.7=10/9 cm³. 

Mass=volume×density.

Volume of B=2.4dm³. 1dm (decimetre)=10cm, so 1dm³=1000cm³.

Volume of B=2400cm³. Mass of B=2400×4.8=11520g.

Total mass of A and B=3+11520=11523g.

Total volume of A and B=10/9+2400=21610/9.

Density=11523×9/21610=4.799g/cm³. This is close to B's density and is expected because B is much more massive than A, so A is almost negligible. However, this is based on the assumption that 1dm=0.1m while 1cm=0.01m.

If dm should have been cm, then the mass of B would have been 2.4×4.8=11.52g.

Total mass of A and B=3+11.52=14.52g.

Total volume of A and B=10/9+2.4=158/45cm³.

Density=14.52×45/158=4.135g/cm³. This seems to me to be the expected answer.