Sure! Let's solve the problem step-by-step.
### Step 1: Identify the given values
- The weight of the rock is [tex]\( 32.0 \, \text{g} \)[/tex].
- The initial volume of water in the graduated cylinder is [tex]\( 12.3 \, \text{mL} \)[/tex].
- The final volume of water after placing the rock in the graduated cylinder is [tex]\( 16.8 \, \text{mL} \)[/tex].
### Step 2: Calculate the displaced volume
The displaced volume is the difference between the final volume and the initial volume.
[tex]\[ \text{Displaced Volume} = \text{Final Volume} - \text{Initial Volume} \][/tex]
[tex]\[ \text{Displaced Volume} = 16.8 \, \text{mL} - 12.3 \, \text{mL} \][/tex]
[tex]\[ \text{Displaced Volume} = 4.5 \, \text{mL} \][/tex]
### Step 3: Calculate the density
The density of the rock can be found using the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Given:
- Mass (weight) of the rock = [tex]\( 32.0 \, \text{g} \)[/tex]
- Displaced Volume = [tex]\( 4.5 \, \text{mL} \)[/tex]
[tex]\[ \text{Density} = \frac{32.0 \, \text{g}}{4.5 \, \text{mL}} \][/tex]
### Step 4: Perform the division and round to the tenths place
[tex]\[ \text{Density} = 7.1 \, \text{g/mL} \][/tex]
So, the density of the rock is [tex]\( 7.1 \, \text{g/mL} \)[/tex].
### Summary
- Displaced Volume: [tex]\( 4.5 \, \text{mL} \)[/tex]
- Density: [tex]\( 7.1 \, \text{g/mL} \)[/tex]
So, the answer to the question is:
[tex]\[
\text{Density} = 7.1 \, \text{g/mL}
\][/tex]
