Iron has a density of 7.86 g/cm3 (1 cm3=1 mL). Calculate the volume (in dL) of a piece of iron having a mass of 3.97 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.
To calculate the volume, we need to convert the given density from g/cm³ to kg/dL.
1 cm³ = 1 mL
1 g/cm³ = 1 kg/L
Since 1 L = 10 dL, we can convert the density as follows:
7.86 g/cm³ * (1 kg/1000 g) * (1000 mL/1 L) * (1 L/10 dL)
Simplifying this:
7.86 * 1/1000 * 1000/1 * 1/10 = 0.786 kg/dL
Now we can use the density in kg/dL to calculate the volume of the iron piece.
Given:
Mass = 3.97 kg
Density = 0.786 kg/dL
We can rearrange the formula for density to solve for volume:
Density = Mass / Volume
Rearranging the formula, we have:
Volume = Mass / Density
Volume = 3.97 kg / 0.786 kg/dL
Simplifying this:
Volume = 5.05 dL
Therefore, the volume of the iron piece is 5.05 dL.
To calculate the volume of the piece of iron, you need to convert the density from g/cm3 to kg/dL.
First, let's convert the density from g/cm3 to g/mL:
Since 1 cm3 = 1 mL, the density of iron remains unchanged when converting from g/cm3 to g/mL.
Now, let's convert g/mL to kg/dL:
1 g = 0.001 kg (since there are 1000 grams in 1 kilogram)
1 mL = 0.1 dL (since there are 10 milliliters in 1 deciliter)
Therefore, 1 g/mL is equivalent to 0.001 kg/0.1 dL, which simplifies to 0.01 kg/dL.
Now that we have expressed the density in the desired units of volume and mass, we can calculate the volume of the piece of iron.
Given mass = 3.97 kg and density = 0.01 kg/dL
We can use the formula: density = mass/volume
Solving for volume: volume = mass / density
Substituting the given values: volume = 3.97 kg / 0.01 kg/dL
Dividing 3.97 by 0.01 gives us a volume of 397 dL.
Therefore, the volume of the piece of iron is 397 dL.
3970 g / 7.86 g/mL = ? mL
100 mL = 1 dL