Final answer:
To find the surface area of a cube given its mass and density, calculate the volume using the mass and density, then find the cube root of the volume for the side length, and use that to calculate the surface area.
Step-by-step explanation:
The question is asking to calculate the surface area of a cube when given the density and mass. From the given density (2.3×1017 kg/m³) and the mass (1.0 kg), one can calculate the volume of the cube since density is mass divided by volume. Once the volume is known, one can derive the length of a side since volume is the cube of the side length for a cube. With the side length known, surface area can be calculated using the formula surface area = 6 × (side length)2.
To calculate the volume (V), use the following steps:
- Determine the volume using the formula V = mass/density.
- Calculate the cube root of the volume to find the side length (s).
- Calculate the surface area using the formula surface area = 6 × s2.
If we go step-by-step using the given mass of 1.0 kg and the density of nuclear matter (2.3×1017 kg/m³), the side length can be derived and subsequently the surface area.