Answer: The volume of the cube is given by V = s^3, where s is the length of each side. Therefore, the volume of the cube is:
V = (3.01 cm)^3 = 27.28 cm^3
The density of the cube is given by the mass divided by the volume:
density = mass / volume = 0.317 kg / 27.28 cm^3
We need to convert cm^3 to kg/m^3 to get the units right:
1 cm^3 = 10^-6 m^3
1 kg/m^3 = 10^6 kg/cm^3
So, we have:
density = 0.317 kg / (27.28 cm^3 x 10^-6 m^3/cm^3)
density = 11,603 kg/m^3
Now, we need to identify the metal. The density of the cube can be compared to the densities of different metals to determine the identity. Here are the densities of some common metals:
- Aluminum: 2,700 kg/m^3
- Copper: 8,960 kg/m^3
- Gold: 19,320 kg/m^3
- Iron: 7,870 kg/m^3
- Lead: 11,340 kg/m^3
- Silver: 10,490 kg/m^3
Since the density of the cube is closest to the density of lead, we can identify the metal as lead.