Final answer:
Cubic units are used to express the volume of a gold nugget measured by the water displacement method because volume is a measure of three-dimensional space.
Step-by-step explanation:
The volume of a gold nugget can be expressed in cubic units because the water displacement method allows for the measurement of the volume of irregularly shaped objects.
When the gold nugget is submerged in water, it displaces an amount of water exactly equal to its own volume due to the principle of buoyancy. This displaced volume can be quantitatively measured, and since volume is a three-dimensional space measurement, it is expressed in cubic units (such as cubic centimeters, cubic meters, etc.).
The concept of density, defined as mass per unit volume, is crucial in understanding why cubic units are appropriate. For gold, which has a density of 19.3 g/cm³, this relationship allows us to use the mass and density of gold to calculate its volume.
As such, if you have a specific mass of gold, you can use its reciprocal density to convert mass into volume by introducing the cubic unit, which corresponds to the physical space the gold occupies.
Similar principles apply to the volume measurement of other materials. For instance, the metric system aligns the density of water to be 1 g/cm³, making it straightforward to translate mass into volume for water as well. This is why we measure the volume of the water displaced by submerging an object, like a gold nugget or a coin, to find its volume in cubic units based on its weight loss in the water.
The principle of buoyancy ensures that the displaced water equals the volume of the submerged nugget, and using the known density of gold, one can calculate this volume based on mass.