Final answer:
The density of aluminum is calculated by dividing the mass (180 g) by the volume (64 cm³) resulting in 2.8125 g/cm³, then rounded to 2.81 g/cm³. However, the provided answer options are incorrect, as experimental data shows the actual density of aluminum is 2.7 g/cm³.
Step-by-step explanation:
The question pertains to finding the density of aluminum given the mass of an aluminum cube and its dimensions. The mass of the aluminum cube is recorded as 180 g and one side of the cube measures 4 cm. To calculate density, which is mass divided by volume, we need to first find the volume of the cube. The volume of a cube with each side measuring 4 cm is calculated by cubing this measurement, resulting in a volume of 64 cm³ (that is, 4 cm × 4 cm × 4 cm).
The density is then calculated by dividing the mass by the volume. Given that the mass is 180 g and the volume is 64 cm³, the resulting density is 2.8125 g/cm³. When rounded to the nearest hundredth to match the options provided in the question, we get 2.81 g/cm³. However, since this option is not available among the choices, it is likely that the given answers are incorrect or that there has been a transcription error in the options. Based on the reference information provided, we know that the experimental density of aluminum is 2.7 g/cm³, confirming that our calculation is accurate and the options provided are not correct.