Question

part c 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 3.22 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

Explanation:

Step1: Convert density to kg/dL

First, convert $\text{g/cm}^3$ to $\text{kg/dL}$:
$1\ \text{kg}=1000\ \text{g}$, $1\ \text{dL}=100\ \text{mL}=100\ \text{cm}^3$
$$7.86\ \frac{\text{g}}{\text{cm}^3} \times \frac{1\ \text{kg}}{1000\ \text{g}} \times \frac{100\ \text{cm}^3}{1\ \text{dL}} = 0.786\ \frac{\text{kg}}{\text{dL}}$$

Step2: Calculate volume from density formula

Density formula: $
ho=\frac{m}{V}$, rearrange to $V=\frac{m}{
ho}$
Substitute $m=3.22\ \text{kg}$ and $
ho=0.786\ \text{kg/dL}$:
$$V=\frac{3.22\ \text{kg}}{0.786\ \text{kg/dL}}$$

Step3: Compute and round to 3 sig figs

Calculate the value and round to three significant figures:
$$V=4.09669\ \text{dL} \approx 4.10\ \text{dL}$$

Answer:

$4.10$ dL