To determine the volume of the diamond, we need to use the formula for density, which is:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Given the density and mass of the diamond, we can rearrange the formula to solve for the volume:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
Substitute the given values into the formula:
- Mass ([tex]\( m \)[/tex]) = 481.3 grams
- Density ([tex]\( \rho \)[/tex]) = 3.51 grams per cubic centimeter
Now, we can calculate the volume:
[tex]\[ \text{Volume} = \frac{481.3 \text{ grams}}{3.51 \text{ grams per cubic centimeter}} \][/tex]
[tex]\[ \text{Volume} = 137.12250712250713 \text{ cubic centimeters} \][/tex]
The problem requires us to round the answer to the nearest hundredth. So, rounding [tex]\( 137.12250712250713 \)[/tex] to the nearest hundredth gives:
[tex]\[ 137.12 \text{ cubic centimeters} \][/tex]
Therefore, the volume of the diamond is:
[tex]\[ \boxed{137.12 \text{ cm}^3} \][/tex]
