Sure, let's work through this problem step-by-step.
1. Understand the Problem:
- We need to find the volume occupied by a piece of aluminum given its mass and its density.
2. Given Data:
- The density of aluminum ([tex]\( \rho \)[/tex]) is 2700 kg/m³.
- The mass of the aluminum piece ([tex]\( m \)[/tex]) is 10 kg.
3. Relevant Formula:
- To find the volume ([tex]\( V \)[/tex]), we can use the relationship between mass, density, and volume. The formula is:
[tex]\[
V = \frac{m}{\rho}
\][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( \rho \)[/tex] is the density.
4. Substitute the Given Values:
- Substitute [tex]\( m = 10 \)[/tex] kg and [tex]\( \rho = 2700 \)[/tex] kg/m³ into the formula.
[tex]\[
V = \frac{10 \text{ kg}}{2700 \text{ kg/m}^3}
\][/tex]
5. Calculate the Volume:
- Perform the division:
[tex]\[
V = \frac{10}{2700}
\][/tex]
6. Simplify the Fraction:
- Simplify the fraction:
[tex]\[
V = 0.003703703703703704 \text{ m}^3
\][/tex]
Therefore, the volume occupied by 10 kg of aluminum is approximately 0.0037 m³ (or exactly 0.003703703703703704 m³ in more detailed precision).
