To find the density of a cube given its mass and side length, follow these steps:
1. Determine the Volume of the Cube:
The volume [tex]\( V \)[/tex] of a cube can be calculated using the formula:
[tex]\[
V = \text{side length}^3
\][/tex]
Given that the side length of the cube is [tex]\( 4.1 \, \text{cm} \)[/tex]:
[tex]\[
V = 4.1^3 = 68.92099999999998 \, \text{cm}^3
\][/tex]
2. Calculate the Density:
Density [tex]\( D \)[/tex] is given by the formula:
[tex]\[
D = \frac{m}{V}
\][/tex]
Where:
[tex]\( m \)[/tex] is the mass of the cube, which is [tex]\( 12.6 \, \text{g} \)[/tex]
[tex]\( V \)[/tex] is the volume of the cube, which we calculated to be [tex]\( 68.92099999999998 \, \text{cm}^3 \)[/tex]
Substitute the values into the formula:
[tex]\[
D = \frac{12.6 \, \text{g}}{68.92099999999998 \, \text{cm}^3} = 0.1828180090248256 \, \text{g/cm}^3
\][/tex]
3. Select the Closest Value:
Comparing this result to the given options:
- [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 closest value is [tex]\( 0.1828 \, \text{g/cm}^3 \)[/tex].
Therefore, the density of the cube is [tex]\( 0.1828 \, \text{g/cm}^3 \)[/tex].
