The density of steel is ρ = 7.86 g/cm 3 . Show the conversion to a value in kg/m3 units.

To convert the density of steel from \( \text{g/cm}^3 \) to \( \text{kg/m}^3 \), we follow these steps:

### Given:
\[
\rho = 7.86 \, \text{g/cm}^3
\]

### Conversion factors:
- \(1 \, \text{g} = 0.001 \, \text{kg}\)
- \(1 \, \text{cm}^3 = 1 \times 10^{-6} \, \text{m}^3\)

### Step-by-Step Conversion:

1. Convert grams to kilograms:
\[
\rho = 7.86 \, \text{g/cm}^3 \times \frac{0.001 \, \text{kg}}{1 \, \text{g}} = 7.86 \times 0.001 \, \text{kg/cm}^3 = 0.00786 \, \text{kg/cm}^3
\]

2. Convert cubic centimeters to cubic meters:
\[
\rho = 0.00786 \, \text{kg/cm}^3 \times \frac{1 \, \text{cm}^3}{1 \times 10^{-6} \, \text{m}^3} = 0.00786 \times 10^6 \, \text{kg/m}^3 = 7860 \, \text{kg/m}^3
\]

### Final Answer:
The density of steel in \( \text{kg/m}^3 \) is \( \rho = 7860 \, \text{kg/m}^3 \).

Would you like to explore this topic further or ask any questions?

Here are some related questions:
1. How does the density of steel compare to other common materials like aluminum or copper?
2. If the volume of a steel rod is known, how can you calculate its mass using the density?
3. What is the importance of converting units in engineering applications?
4. How would the density change if we consider different grades of steel?
5. How does temperature affect the density of materials like steel?

**Tip:** Always ensure unit consistency in calculations to avoid errors, especially in engineering and scientific computations.

Learn how to convert the density of steel from grams per cubic centimeter (g/cm^3) to kilograms per cubic meter (kg/m^3) with a detailed step-by-step solution. This problem covers unit conversion and density calculation. Ideal for high school students and anyone interested in engineering applications.

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