ron has a density of \( 7.87 \mathrm{~g} / \mathrm{cm}^{3} \). Calculate the mass of an iron sample with a volume of \( 4.09 \times 10^{-5} \mathrm{~m}^{3} \).

To calculate the mass of the iron sample, we can use the formula: \[ \text{mass} = \text{density} \times \text{volume} \] First, we need to ensure that the units are consistent. The density of iron is given in grams per cubic centimeter (\( \mathrm{g/cm}^3 \)), and the volume is given in cubic meters (\( \mathrm{m}^3 \)). We can convert the volume from cubic meters to cubic centimeters: \[ 1 \, \mathrm{m}^3 = 10^6 \, \mathrm{cm}^3 \] Thus, the volume in cubic centimeters is: \[ 4.09 \times 10^{-5} \, \mathrm{m}^3 = 4.09 \times 10^{-5} \times 10^6 \, \mathrm{cm}^3 = 4.09 \times 10^{1} \, \mathrm{cm}^3 = 40.9 \, \mathrm{cm}^3 \] Now we can use the density of iron to find the mass: \[ \text{mass} = 7.87 \, \mathrm{g/cm}^3 \times 40.9 \, \mathrm{cm}^3 \] Calculating this gives: \[ \text{mass} = 7.87 \times 40.9 = 321.823 \, \mathrm{g} \] Therefore, the mass of the iron sample is approximately: \[ \text{mass} \approx 321.82 \, \mathrm{g} \]