Question

Iron has a density of 7.86 g/cm3. Calculate the volume (in dL) of a piece of iron having a mass of 4.07 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 a 4.07 kg piece of iron given its density, convert the density to kg/dL and divide the mass by this converted density. The volume is determined to be 5.18 dL.

Step-by-step explanation:

To calculate the volume of a piece of iron with a mass of 4.07 kg when the density of iron is 7.86 g/cm³, we need to convert the given density into kg/dL first. Since 1 cm³ is equal to 1 mL and there are 1000 mL in a liter (L), and 1 dL is 1/10 of a liter, we can find the density in kg/dL. We also have to convert grams to kilograms, knowing that there are 1000 grams in a kilogram.

First, convert the density from g/cm³ to g/dL:

7.86 g/cm³ = 786 g/dL (because 1 dL = 100 cm³)

Now, convert g/dL to kg/dL:

786 g/dL = 0.786 kg/dL

Now, use the mass of the iron (4.07 kg) and divide it by the density in kg/dL to find the volume:

Volume = Mass / Density

Volume = 4.07 kg / 0.786 kg/dL

Volume = 5.18 dL

Therefore, a piece of iron that weighs 4.07 kg will have a volume of 5.18 dL.