Final answer:
To differentiate between the circumference and the area formulas of a circle, consider that circumference has units of length and uses the formula C = 2πr, while area has squared units and uses the formula A = πr².
Step-by-step explanation:
When trying to recall the formula for the circumference of a circle or its area, it's useful to consider the units involved. The circumference is a linear measurement, which means its units would be in terms of length, such as meters (m). The area, on the other hand, is a two-dimensional measurement, meaning its units are squared, like square meters (m²).
The formula for the circumference is C = 2πr (where C is the circumference and r is the radius), and it yields a linear measurement. Thus, if you think of πr², since it has a square in the formula, it must represent an area, because that square indicates that you are working with two dimensions.
Essentially, look at the units: if you're seeking a linear measurement, you will not include a square in your computation, whereas a two-dimensional area will include squared units. This is why the area of a circle is A = πr² (where A is the area).