Final answer:
To find the mass of a hollow sphere of copper, calculate the volume using the formula for a hollow sphere and multiply it by the density of copper. The mass is approximately 334.93 g.
Step-by-step explanation:
To find the mass of a hollow sphere of copper, we need to calculate the volume of the hollow sphere and then multiply it by the density of copper. The volume of a hollow sphere is calculated using the formula V = (4/3)π(R^3 - r^3), where R is the external radius and r is the internal radius. In this case, the external diameter is 12 cm, so the external radius is 6 cm, and the internal diameter is 11.8 cm, so the internal radius is 5.9 cm.
Substituting these values into the formula, we get V = (4/3)π((6^3) - (5.9^3)) = (4/3)π(216 - 206.969) = (4/3)π(9.031) ≈ 37.71 cm³.
Given that 1 cm³ of copper has a mass of 8.88 g, the mass of the hollow sphere is approximately 37.71 cm³ × 8.88 g/cm³ ≈ 334.93 g. Therefore, the correct option is Option 3: 180.15 g.