To find the density of a cube with a given mass and side length, we will follow a detailed step-by-step process.
### Step 1: Understand the Problem
We are given:
- Mass of the cube: [tex]\( 12.6 \)[/tex] grams
- Side length of the cube: [tex]\( 4.1 \)[/tex] cm
We need to determine the density of the cube. The formula for density ([tex]\( D \)[/tex]) is given by:
[tex]\[ D = \frac{m}{v} \][/tex]
where:
- [tex]\( m \)[/tex] is the mass
- [tex]\( v \)[/tex] is the volume
### Step 2: Calculate the Volume of the Cube
The volume ([tex]\( v \)[/tex]) of a cube with side length [tex]\( a \)[/tex] is calculated using the formula:
[tex]\[ v = a^3 \][/tex]
Given the side length ([tex]\( a \)[/tex]) is [tex]\( 4.1 \)[/tex] cm, the volume of the cube is:
[tex]\[ v = (4.1 \, \text{cm})^3 \][/tex]
From calculations (previously obtained):
[tex]\[ v \approx 68.921 \, \text{cm}^3 \][/tex]
### Step 3: Calculate the Density
Using the mass [tex]\( m = 12.6 \)[/tex] grams and the volume [tex]\( v = 68.921 \)[/tex] cm[tex]\(^3\)[/tex], we can find the density:
[tex]\[ D = \frac{12.6 \, \text{g}}{68.921 \, \text{cm}^3} \][/tex]
[tex]\[ D \approx 0.1828 \, \text{g/cm}^3 \][/tex]
### Step 4: Identify the Correct Answer
Given the choices provided:
1. [tex]\( 0.1828 \, \text{g/cm}^3 \)[/tex]
2. [tex]\( 3.073 \, \text{g/cm}^3 \)[/tex]
3. [tex]\( 68.92 \, \text{g/cm}^3 \)[/tex]
The correct density of the cube is:
[tex]\[ 0.1828 \, \text{g/cm}^3 \][/tex]
### Conclusion
Thus, the density of the cube is:
[tex]\[ 0.1828 \, \text{g/cm}^3 \][/tex]
