A sample of a metal is placed in a graduated cylinder to find the volume by water displacement . The water level rises from 15.3 mL to 24.4 mL. The sample of the metal is weighed on a balance, and the mass is determined to be 40.972 q. What is the density of the metal? 5g/mL 4.5g/mL 4.502g/mL 4.50g/mL

To find the density of the metal, we need to use the formula for density:<br /><br />\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]<br /><br />First, let's determine the volume of the metal. The volume is found by the water displacement method, which is the difference in the water level before and after the metal is added.<br /><br />Initial water level: 15.3 mL <br />Final water level: 24.4 mL <br /><br />Volume of the metal:<br />\[ \text{Volume} = 24.4 \, \text{mL} - 15.3 \, \text{mL} = 9.1 \, \text{mL} \]<br /><br />Next, we have the mass of the metal:<br />\[ \text{Mass} = 40.972 \, \text{g} \]<br /><br />Now, we can calculate the density:<br />\[ \text{Density} = \frac{40.972 \, \text{g}}{9.1 \, \text{mL}} \approx 4.502 \, \text{g/mL} \]<br /><br />Therefore, the correct answer is:<br />\[ 4.502 \, \text{g/mL} \]