Let's solve the problem step by step by calculating the density for each rock sample and then determining its type based on the given density ranges.
### Step 1: Calculate the Densities
We start by using the formula for density:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
#### Sample 1:
Mass = 1.17 g
Volume = 0.33 cm³
[tex]\[ \text{Density}_1 = \frac{1.17 \text{ g}}{0.33 \text{ cm}^3} = 3.545454545454545 \text{ g/cm}^3 \][/tex]
#### Sample 2:
Mass = 2.7 g
Volume = 1.1 cm³
[tex]\[ \text{Density}_2 = \frac{2.7 \text{ g}}{1.1 \text{ cm}^3} = 2.4545454545454546 \text{ g/cm}^3 \][/tex]
#### Sample 3:
Mass = 11.2 g
Volume = 1.9 cm³
[tex]\[ \text{Density}_3 = \frac{11.2 \text{ g}}{1.9 \text{ cm}^3} = 5.894736842105263 \text{ g/cm}^3 \][/tex]
### Step 2: Determine the Rock Types
Next, we compare the calculated densities with the given density ranges for different minerals.
#### Sample 1:
Density = 3.545454545454545 g/cm³
According to the table:
- Diamond: 3.50-3.55 g/cm³
This density falls within the range for Diamond. Thus, Sample 1 is a Diamond.
#### Sample 2:
Density = 2.4545454545454546 g/cm³
According to the table:
- Common glass: 2.40-2.80 g/cm³
This density falls within the range for Common glass. Thus, Sample 2 is Common glass.
#### Sample 3:
Density = 5.894736842105263 g/cm³
According to the table:
- Cubic zirconia: 5.50-5.90 g/cm³
This density falls within the range for Cubic zirconia. Thus, Sample 3 is Cubic zirconia.
### Conclusion
Summarizing the findings:
1. If a rock sample has a mass of 1.17 g and a volume of 0.33 cm³, it is a Diamond.
2. If a rock sample has a mass of 2.7 g and a volume of 1.1 cm³, it is Common glass.
3. If a rock sample has a mass of 11.2 g and a volume of 1.9 cm³, it is Cubic zirconia.
