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Question 9 (Fill-In-The-Blank Worth 4 points)

A large emerald with a mass of 982.7 grams was recently discovered in a mine. If the density of the emerald is [tex]$2.76 \frac{\text{grams}}{\text{cm}^3}$[/tex], what is the volume? Round to the nearest hundredth when necessary, and only enter numerical values, which can include a decimal point.

Answer for Blank 1:



Answer :

GinnyAnswer
To determine the volume of a large emerald given its mass and density, we need to use the formula for volume based on mass and density:

[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]

Given data:
- Mass of the emerald [tex]\( = 982.7 \)[/tex] grams
- Density of the emerald [tex]\( = 276 \frac{\text{grams}}{\text{cm}^3} \)[/tex]

Substitute the given values into the formula:

[tex]\[ \text{Volume} = \frac{982.7}{276} \][/tex]

Perform the division:

[tex]\[ \frac{982.7}{276} \approx 3.5605072463768117 \][/tex]

We need to round the volume to the nearest hundredth:

[tex]\[ \text{Volume} \approx 3.56 \][/tex]

Thus, the volume of the emerald is:

[tex]\[ 3.56 \ \text{cm}^3 \][/tex]

Answer for Blank 1: 3.56

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