To determine the volume of a gold nugget with a mass of 13 grams and a density of 19.3 g/cm³, we can use the relationship between density (D), mass (m), and volume (v) given by the formula:
[tex]\[ D = \frac{m}{v} \][/tex]
First, we need to isolate the volume (v) in the formula. To do this, we rearrange the formula to solve for volume:
[tex]\[ v = \frac{m}{D} \][/tex]
Now, we substitute the given values for mass (m = 13 grams) and density (D = 19.3 g/cm³):
[tex]\[ v = \frac{13 \, \text{g}}{19.3 \, \text{g/cm}^3} \][/tex]
Performing the division:
[tex]\[ v = 0.6735751295336787 \, \text{cm}^3 \][/tex]
Therefore, the volume of a 13 g gold nugget with a density of 19.3 g/cm³ is approximately 0.674 cm³. Among the given options, the closest value is:
[tex]\[ 0.67 \, \text{cm}^3 \][/tex]
So, the correct answer is:
[tex]\[ 0.67 \, \text{cm}^3 \][/tex].
