Question

iron has a density of 7.86 g/cm3 . 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 cm3 = 1 mL ) before calculating the volume for the piece of iron.

Answer 1

To calculate the volume of the piece of iron, we need to divide its mass by its density. But first, we need to express the density in the same units as the mass, which is kg/dL. To do this, we need to convert the density from g/cm3 to kg/dL.

1 cm3 = 1 mL = 0.001 L

1 dL = 0.1 L

Therefore, 1 cm3 = 0.001 L = 0.1 dL

Also, 1 g = 0.001 kg

Therefore,

density in kg/dL = (density in g/cm3) * (1 kg/1000 g) * (0.1 dL/1 cm3)

= 7.86 g/cm3 * 0.001 kg/g * 0.1 dL/cm3

= 0.00786 kg/dL

Now we can use this density to calculate the volume of the piece of iron:

Volume = mass / density

= 4.62 kg / 0.00786 kg/dL

= 5892.9 dL

So, the volume of the piece of iron is 5892.9 dL.