Question

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 g/cm³, what is the volume? round your answer to the nearest hundredth.

Explanation:

Step1: Recall the density formula

Density formula is \(
ho=\frac{m}{V}\), where \(
ho\) is density, \( m\) is mass and \( V\) is volume. We need to solve for \( V\), so \( V = \frac{m}{
ho}\).

Step2: Substitute the given values

Given \( m = 2138.7\space g\) and \(
ho=3.51\space g/cm^{3}\). Then \( V=\frac{2138.7}{3.51}\).

Step3: Calculate the value

\( \frac{2138.7}{3.51}=609.3162393\). Rounding to the nearest hundredth gives \( V = 609.32\space cm^{3}\).

Answer:

\(609.32\space cm^{3}\)