Question

Iron has a density of 7.86 g/cm^3 (1 cm^3=1 mL). Calculate the volume (in dL) of a piece of iron having a mass of 4.62 kg . Note that the density is provided in different units of volume and mass than the desired units of volume (dL) and the given units of mass (kg). You will need to express the density in kg/dL (1 cm^3 = 1 mL) before calculating the volume for the piece of iron.

Answer 1

Density is mass over volume. The density of iron is given in g/cm³

we have to first convert g/cm³ to kg/dL.

1000 g = 1 kg and 100 cm³ = 1 dL

the mass of 1 cm³ = 1 g

the mass of 100 cm³ / 1 dL = 100 g

then mass of 1 dL in kg is = 100 g / 1000 g/kg = 0.1 kg

volume of 0.1 kg is 1 dL

therefore density of iron is 7.86 g/cm³ x 0.1 kg/dL / g/cm³ = 0.786 kg/dL

volume of iron having mass 0.786 kg is 1 dL

then volume of iron having a mass of 4.62 kg is - 1 dL / 0.786 kg x 4.62 kg = dL

volume of iron is 5.88 dL