Question

iron has a density of 7.86 g/cm³. calculate the volume (in dl) of a piece of iron having a mass of 3 39 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. express your answer to three significant figures. view available hint(s) volume = dl. submit previous answers incorrect; try again; 4 attempts remaining

Explanation:

Step1: Convert density to kg/dL

We know that \(1\space g = 10^{- 3}\space kg\) and \(1\space cm^{3}=1\space mL = 10^{-2}\space dL\) (since \(1\space dL = 100\space mL\)).
The density of iron is \(
ho=7.86\space g/cm^{3}\).
First, convert grams to kilograms: \(7.86\space g=7.86\times10^{-3}\space kg\).
Then, convert \(cm^{3}\) to \(dL\): \(1\space cm^{3} = 10^{-2}\space dL\).
So the density in \(kg/dL\) is \(
ho=\frac{7.86\times 10^{-3}\space kg}{10^{-2}\space dL}=0.786\space kg/dL\).

Step2: Use density formula to find volume

The density formula is \(
ho=\frac{m}{V}\), where \(m\) is mass and \(V\) is volume. We can rearrange it to \(V = \frac{m}{
ho}\).
The mass of the iron piece \(m = 3.39\space kg\) and \(
ho=0.786\space kg/dL\).
Substitute the values: \(V=\frac{3.39\space kg}{0.786\space kg/dL}\approx4.31\space dL\) (to three significant figures).

Answer:

\(4.31\)