Final answer:
The independent variable is the amount of sugar, the dependent variable is the temperature or state of the water, and the constant is the heating applied.
Step-by-step explanation:
When sugar is heated in a cup of water, the independent variable would be the amount of sugar, because it is what the researcher or experimenter is manipulating. The dependent variable would be the temperature or state of the water, as it is expected to change in response to the amount of sugar added. The constant in this experiment would be the heat applied, as it should remain consistent to ensure reliable results.
The correct identification of variables is as follows: Independent Variable: Sugar; Dependent Variable: Temperature or state of the water; Constant: Heating. Thus, the correct option in the given choices would be Independent: Sugar; Dependent: Cup of water (Temperature/State); Constant: Heating.