Which expression represents the area of a circle with radius r?

• A. A = πr^2
• B. A = 2πr
• C. C = πr^2
• D. C = 2πr

Answer: (A)

The main idea here is how the area of a circle depends on its radius. The area grows with the square of the radius, and the standard formula that captures this relationship is A = π r^2. This comes from imagining the circle’s area built up from infinitesimal rings or by noticing that scaling the radius by a factor k makes the area scale by k^2. So if you double the radius, the area becomes four times as large; if you triple the radius, it becomes nine times as large. The symbol A is used for area, and π is the constant that relates a circle’s radius to its area through this squared relationship.

The other options mix up what’s being calculated or the notation. 2πr is the formula for the circle’s circumference, not its area. Writing C = πr^2 or C = 2πr uses a different letter for the area, which isn’t standard, since A = πr^2 is the correct expression for area.