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Question 1 (Multiple Choice, Worth 1 point)

A large diamond with a mass of [tex]$2138.7 \, \text{grams}$[/tex] was recently discovered in a mine. If the density of the diamond is [tex]$3.51 \frac{\text{g}}{\text{cm}^3}$[/tex], what is the volume? Round your answer to the nearest hundredth.

A. [tex][tex]$141.84 \, \text{cm}^3$[/tex][/tex]
B. [tex]$609.32 \, \text{cm}^3$[/tex]
C. [tex]$717.06 \, \text{cm}^3$[/tex]
D. [tex][tex]$8169.8 \, \text{cm}^3$[/tex][/tex]

Question 2 (Multiple Choice, Worth 1 point)



Answer :

GinnyAnswer
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]

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