To determine the density of a cube given its mass and side length, follow these steps:
1. Understand the given data:
- Mass ([tex]\( m \)[/tex]) of the cube: 12.6 grams
- Side length of the cube ([tex]\( \text{side length} \)[/tex]): 4.1 centimeters
2. Calculate the volume of the cube:
The formula for the volume ([tex]\( V \)[/tex]) of a cube is given by:
[tex]\[
V = \text{side length}^3
\][/tex]
Plug in the side length:
[tex]\[
V = 4.1^3
\][/tex]
Evaluating this, we find:
[tex]\[
V \approx 68.921 \, \text{cm}^3
\][/tex]
3. Calculate the density:
Density ([tex]\( D \)[/tex]) is defined as mass ([tex]\( m \)[/tex]) divided by volume ([tex]\( V \)[/tex]):
[tex]\[
D = \frac{m}{V}
\][/tex]
Substitute the values of mass and volume:
[tex]\[
D = \frac{12.6 \, \text{g}}{68.921 \, \text{cm}^3}
\][/tex]
Performing the division, we get:
[tex]\[
D \approx 0.1828 \, \text{g/cm}^3
\][/tex]
4. Compare the calculated density with the given choices:
- [tex]\( 0.1828 \, \text{g/cm}^3 \)[/tex]
- [tex]\( 0.3254 \, \text{g/cm}^3 \)[/tex]
- [tex]\( 3.073 \, \text{g/cm}^3 \)[/tex]
- [tex]\( 68.92 \, \text{g/cm}^3 \)[/tex]
The calculated density, approximately [tex]\( 0.1828 \, \text{g/cm}^3 \)[/tex], matches one of the given choices:
[tex]\[
0.1828 \, \text{g/cm}^3
\][/tex]
Thus, the correct answer is [tex]\( 0.1828 \, \text{g/cm}^3 \)[/tex].
