Final answer:
The beaker of water being three-dimensional pertains to the liquid's property of having a definite volume but an indefinite shape. It also refers to the three-dimensional space that the liquid occupies. Density is an associated intensive property of matter, exemplified by water's consistent density of 1.0 g/mL.
Step-by-step explanation:
When recalling that a beaker of water is three-dimensional, we are considering its property of being a liquid. This means that it has a definite volume but an indefinite shape, conforming to the shape of the container it occupies. Understanding this physical state is crucial in the study of matter, especially when distinguishing between different states such as solids, liquids, and gases. The length is a measure that applies to one dimension of an object, and it helps in determining the object's volume when combined with width and height for geometrical solids, or as a volume measure for liquids in containers like beakers. Density is a critical intensive property of matter, defined as the mass-to-volume ratio and remains constant regardless of the sample size. For example, water has a density of 1.0 g/mL, and this density retains its value whether the water is in a small glass or a large swimming pool. When we talk about a beaker of water being three-dimensional, we are often discussing this property related to the volume that the liquid occupies. Additionally, it refers to the liquid's property of taking up space in three dimensions which is a fundamental aspect of matter in the liquid state.