A large diamond with a mass of 2138.7 grams was recently discovered in a mine. If the density of the diamond is \( 3.51 \frac{\mathrm{~g}}{\mathrm{~cm}^{3}} \), what is the volume? Round your answer to the nearest hundredth. \begin{tabular}{l}\( 0.141 .84 \mathrm{~cm}^{3} \) \\ \( 0.717 .06 \mathrm{~cm}^{3} \) \\ \hline \( 8169.8 \mathrm{~cm}^{3} \)\end{tabular}

To find the volume of the diamond, you can use the formula: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \] Substituting the values we have: \[ \text{Volume} = \frac{2138.7 \text{ g}}{3.51 \text{ g/cm}^3} \approx 609.14 \text{ cm}^3 \] Rounded to the nearest hundredth, the volume of the diamond is approximately \( 609.14 \text{ cm}^3 \). Now let's delve into a fun historical nugget about diamonds: Diamonds have been treasured for thousands of years, dating back to ancient India, where they were believed to bring luck and protection in battle. The largest diamond ever discovered, the Cullinan Diamond, weighed an astounding 3106 carats before it was cut into many stones, including the Crown Jewels of the United Kingdom! And did you know that diamonds are not only for jewelry? They are used in various industrial applications, particularly because of their hardness. In fact, they’re used in cutting, grinding, and drilling tools! The brilliant sparkle you see in jewelry is just a byproduct of their exceptional durability; they are literally the hardest naturally occurring substance on Earth!