If the density of copper is 8.9 g/cm³, what is its density in kg/m³?

Steps to Solve

1. Know the conversion factors

First, we need to know the conversion relationships between grams and kilograms, as well as cubic centimeters and cubic meters:

• 1 kilogram (kg) = 1000 grams (g)
• 1 cubic meter (m³) = 1,000,000 cubic centimeters (cm³)

2. Convert grams to kilograms

To convert the density of copper, which is given in g/cm³, to kg/m³, we will need to divide by 1000 to convert grams to kilograms:

$$ \text{Density in kg/m³} = \frac{\text{Density in g/cm³}}{1000} $$

3. Convert cubic centimeters to cubic meters

Since we are converting from g/cm³ to kg/m³, we also convert cm³ to m³. There are 1,000,000 cm³ in 1 m³, so we will multiply the density by 1,000,000:

$$ \text{Density in kg/m³} = \text{Density in g/cm³} \times 1,000,000 $$

4. Combine the conversions

Since we need to apply both conversions in one step:

$$ \text{Density in kg/m³} = \text{Density in g/cm³} \times \frac{1,000,000}{1000} $$

5. Final adjustment

The fraction simplifies to:

$$ \text{Density in kg/m³} = \text{Density in g/cm³} \times 1000 $$

Now, typically the density of copper is around 8.96 g/cm³. Thus, to find the density in kg/m³:

$$ \text{Density in kg/m³} = 8.96 \times 1000 $$

6. Calculate the final density in kg/m³

Now we can calculate:

$$ 8.96 \times 1000 = 8960 $$

This gives the final density in kg/m³.