Answer :
The most likely identity of the metal is lead.
[tex]\text{Density} = \frac{\text{Mass}}{\text{Volume}}[/tex]
Step 1: Calculate the Volume of the Cube
Given that the side length of the cube is 1.61 mm, we can convert this measurement to centimeters since density is typically expressed in g/cm³. There are 10 mm in 1 cm, so:
[tex]1.61 \text{ mm} = \frac{1.61}{10} = 0.161 \text{ cm}[/tex]
The volume of a cube is calculated using the formula:
[tex]\text{Volume} = \text{side length}^3[/tex]
Substituting the side length:
[tex]\text{Volume} = (0.161 \text{ cm})^3 = 0.004186 \text{ cm}^3[/tex]
Step 2: Convert the Mass to Grams
The mass of the cube is given as 51.7 mg. To convert this to grams:
[tex]51.7 \text{ mg} = \frac{51.7}{1000} = 0.0517 \text{ g}[/tex]
Step 3: Calculate the Density
Now that we have both the mass and the volume in the proper units, we can calculate the density:
[tex]\text{Density} = \frac{0.0517 \text{ g}}{0.004186 \text{ cm}^3} \approx 12.34 \text{ g/cm}^3[/tex]
Step 4: Identify the Metal
Now that we have calculated the density, we can compare this value to known densities of various metals.
- Gold: Approximately 19.32 g/cm³
- Silver: Approximately 10.49 g/cm³
- Copper: Approximately 8.96 g/cm³
- Lead: Approximately 11.34 g/cm³
Based on our calculated density of approximately 12.34 g/cm³, the unknown metal is most likely lead since its density is quite close to the calculated value while remaining consistent with metals density range.
Final answer:
The most likely identity of the metal can be determined by calculating its density using the given mass and side length of the cube.
Explanation:
The most likely identity of the metal can be determined by calculating the density of the cube. Density is defined as mass divided by volume. Since the cube has a mass of 51.7 mg and a side length of 1.61 mm, we can calculate the volume of the cube by cubing the side length (1.61 mm * 1.61 mm * 1.61 mm) and converting it to cubic centimeters (cm³). Then, we divide the mass by the volume to find the density in g/cm³. By comparing the calculated density to the known densities of different metals, we can determine the most likely identity of the metal.
