The density of iron is 7.86 g/cm3. What is the volume in milliliters (mL) of an irregularly shaped piece of iron that has a mass of 524 g?
The Correct Answer and Explanation is:
To find the volume of an irregularly shaped piece of iron, we use the formula:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
We are given:
- Mass = 524 grams
- Density = 7.86 grams per cubic centimeter (g/cm³)
Substitute the values into the formula:Volume=524 g7.86 g/cm3=66.67 cm3\text{Volume} = \frac{524 \, \text{g}}{7.86 \, \text{g/cm}^3} = 66.67 \, \text{cm}^3Volume=7.86g/cm3524g=66.67cm3
Since 1 cm³ is equal to 1 milliliter (mL), the volume is:66.67 mL\boxed{66.67 \, \text{mL}}66.67mL
Explanation:
To solve problems involving density, mass, and volume, it is essential to understand the relationship between these three physical properties. Density is a measure of how much mass is packed into a certain volume. It is calculated using the formula:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Rearranging this formula to find volume gives:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
This formula works for all substances, including irregularly shaped solids such as this piece of iron. Since the mass is given in grams and the density in grams per cubic centimeter, we can perform the calculation directly without any unit conversions. Once we compute the volume in cubic centimeters, we can confidently state the answer in milliliters because 1 cubic centimeter is equivalent to 1 milliliter. This equivalence is based on how volume and liquid measurements are defined in the metric system. Therefore, the final answer for the volume of this 524 gram piece of iron is 66.67 milliliters.
