To find the volume of a diamond given its mass and density, we can use the formula for density:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Rearranging the formula to solve for volume, we get:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
Given:
- Mass of the diamond, [tex]\( \text{Mass} = 2138.7 \)[/tex] grams
- Density of the diamond, [tex]\( \text{Density} = 3.51 \, \frac{\text{g}}{\text{cm}^3} \)[/tex]
Substitute these values into the formula:
[tex]\[ \text{Volume} = \frac{2138.7 \, \text{g}}{3.51 \, \frac{\text{g}}{\text{cm}^3}} \][/tex]
Calculate the volume:
[tex]\[ \text{Volume} \approx 609.3162393162393 \, \text{cm}^3 \][/tex]
Next, round this volume to the nearest hundredth:
[tex]\[ \text{Volume} \approx 609.32 \, \text{cm}^3 \][/tex]
So, the volume of the diamond is:
[tex]\[ \boxed{609.32 \, \text{cm}^3} \][/tex]
