Which of the following expressions represents the area of a circle?

The area of a circle is represented by the formula πr squared, where r denotes the radius of the circle. This formula arises from the mathematical principles relating to circles and takes into account the circular shape and the constant π (pi), which approximates to 3.14159.

To understand why the area is calculated this way, consider that the area essentially measures the space enclosed within the boundary of the circle. The factor of r squared indicates that as the radius increases, the area increases with the square of that increase, illustrating how changes in radius can lead to significant changes in the overall area.

Reviewing the expressions provided:

• The expression involving πd squared does not correctly reflect the area since it incorrectly applies the diameter instead of the radius and is squared inappropriately for area calculation.
• The expression πr represents the circumference of a circle, not the area.
• The expression 2πr is also associated with circumference.

Thus, the expression that accurately represents the area of a circle incorporates the radius squared, confirming that the correct answer is the one expressing it as πr squared.