To find the volume of the emerald, we can use the formula:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
Given the mass of the emerald is 812.04 grams and the density is [tex]\(2.76 \, \text{grams/cm}^3\)[/tex], we substitute these values into the formula:
[tex]\[ \text{Volume} = \frac{812.04 \, \text{grams}}{2.76 \, \text{grams/cm}^3} \][/tex]
By performing the division, we obtain the volume in cubic centimeters.
[tex]\[ \text{Volume} = 294.20289855 \, \text{cm}^3 \][/tex]
Rounding this value to the nearest hundredth:
[tex]\[ \text{Volume} \approx 294.22 \, \text{cm}^3 \][/tex]
Thus, the volume of the emerald is:
[tex]\[ 294.22 \, \text{cm}^3 \][/tex]
