The density of copper is 8.961 x 103 kg/m³. Convert it into g/mL
The correct answer and explanation is :
To convert the density of copper from ( \text{kg/m}^3 ) to ( \text{g/mL} ), we need to follow these steps:
Given:
Density of copper = ( 8.961 \times 10^3 \, \text{kg/m}^3 )
Step 1: Conversion from kg to g
1 kg = 1000 grams. So, to convert the mass from kilograms to grams, we multiply by 1000.
[
8.961 \times 10^3 \, \text{kg} = 8.961 \times 10^3 \times 1000 \, \text{g} = 8.961 \times 10^6 \, \text{g}
]
Step 2: Conversion from cubic meters to milliliters
We need to convert the volume from cubic meters (m³) to milliliters (mL). Since:
[
1 \, \text{m} = 100 \, \text{cm} = 10^2 \, \text{cm}
]
and
[
1 \, \text{m}^3 = 10^6 \, \text{cm}^3 = 10^3 \, \text{mL}
]
Thus,
[
1 \, \text{m}^3 = 10^6 \, \text{mL}
]
Step 3: Apply the conversion factors
Now, we convert the density from ( \text{kg/m}^3 ) to ( \text{g/mL} ). The density in kg/m³ can be converted to g/mL by dividing by ( 10^3 ) (because 1 m³ = ( 10^6 ) mL, and 1 kg = 1000 g):
[
\text{Density in g/mL} = \frac{8.961 \times 10^6 \, \text{g}}{10^6 \, \text{mL}} = 8.961 \, \text{g/mL}
]
Final Answer:
The density of copper is ( \mathbf{8.961} \, \text{g/mL} ).
Explanation:
This conversion involves two primary steps: first converting the mass from kilograms to grams and then converting the volume from cubic meters to milliliters.
- Kilograms to grams: Since 1 kilogram is equal to 1000 grams, we multiply the given density in kg by 1000 to convert to grams. This increases the magnitude of the mass value by a factor of 1000.
- Cubic meters to milliliters: A cubic meter contains 1 million milliliters (since 1 m = 100 cm and 1 m³ = ( 100 \times 100 \times 100 = 10^6 ) cm³, and 1 cm³ = 1 mL). Therefore, to convert density in kg/m³ to g/mL, we divide by ( 10^3 ) because there are ( 10^3 ) milliliters in a liter and ( 10^6 ) milliliters in a cubic meter.
Thus, we arrive at the density of copper in g/mL as ( 8.961 \, \text{g/mL} ).