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Answer :
Sure, I'd be happy to help you understand how to solve this problem step-by-step.
### Step-by-Step Solution:
1. Understand the Problem:
- We are given the mass of an aluminum cube, which is 176 g.
- We are also given the length of one side of the cube, which is 4 cm.
- We need to find the density of the aluminum.
2. Recall the Formula for Density:
- Density ([tex]\( \rho \)[/tex]) is calculated using the formula:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
3. Calculate the Volume of the Cube:
- The volume (V) of any cube is given by the formula:
[tex]\[
\text{Volume} = \text{side length}^3
\][/tex]
- Given the side length of the cube is 4 cm, the volume can be calculated as:
[tex]\[
\text{Volume} = 4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm} = 64 \, \text{cm}^3
\][/tex]
4. Calculate the Density:
- Now that we have both the mass (176 g) and the volume (64 cm³), we can find the density using the formula from step 2.
- Plug in the values:
[tex]\[
\text{Density} = \frac{176 \, \text{g}}{64 \, \text{cm}^3} \approx 2.75 \, \text{g/cm}^3
\][/tex]
### Conclusion:
- The density of the aluminum cube is [tex]\( 2.75 \, \text{g/cm}^3 \)[/tex].
This result allows us to understand that, given the mass and dimensions of the cube, the density measures the amount of mass per unit volume within the aluminum material.
### Step-by-Step Solution:
1. Understand the Problem:
- We are given the mass of an aluminum cube, which is 176 g.
- We are also given the length of one side of the cube, which is 4 cm.
- We need to find the density of the aluminum.
2. Recall the Formula for Density:
- Density ([tex]\( \rho \)[/tex]) is calculated using the formula:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
3. Calculate the Volume of the Cube:
- The volume (V) of any cube is given by the formula:
[tex]\[
\text{Volume} = \text{side length}^3
\][/tex]
- Given the side length of the cube is 4 cm, the volume can be calculated as:
[tex]\[
\text{Volume} = 4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm} = 64 \, \text{cm}^3
\][/tex]
4. Calculate the Density:
- Now that we have both the mass (176 g) and the volume (64 cm³), we can find the density using the formula from step 2.
- Plug in the values:
[tex]\[
\text{Density} = \frac{176 \, \text{g}}{64 \, \text{cm}^3} \approx 2.75 \, \text{g/cm}^3
\][/tex]
### Conclusion:
- The density of the aluminum cube is [tex]\( 2.75 \, \text{g/cm}^3 \)[/tex].
This result allows us to understand that, given the mass and dimensions of the cube, the density measures the amount of mass per unit volume within the aluminum material.
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