To find the volume of the diamond, given its mass and density, follow these steps:
1. Identify the given values:
- Mass of the diamond, [tex]\( \text{mass} = 2138.7 \)[/tex] grams
- Density of the diamond, [tex]\( \text{density} = 3.51 \)[/tex] grams per cubic centimeter ([tex]\( \frac{\text{g}}{\text{cm}^3} \)[/tex])
2. Formula for volume:
The volume ([tex]\( V \)[/tex]) can be calculated using the formula:
[tex]\[
V = \frac{\text{mass}}{\text{density}}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
V = \frac{2138.7 \ \text{grams}}{3.51 \ \frac{\text{grams}}{\text{cm}^3}}
\][/tex]
4. Perform the division:
[tex]\[
V = 609.3162393162393 \ \text{cm}^3
\][/tex]
5. Round the result to the nearest hundredth:
[tex]\[
V \approx 609.32 \ \text{cm}^3
\][/tex]
Therefore, the volume of the diamond, rounded to the nearest hundredth, is [tex]\( \mathbf{609.32 \ cm^3} \)[/tex].
So, the correct multiple choice answer is:
- [tex]\( 609.32 \ cm^3 \)[/tex]
